You have a problem, let's call it problem #4, but we'll discuss that in a later. First, let's discuss what you mean by "low level" electrical applications
Ignoring the issue I'll bring up momentarily, a "low level" electrical application differs from a "thinking machine" application from a physics standpoint in only two ways:
"Low level" electrical applications have long wires.
"Thinking machines" depend heavily (but less every day) on magnetism.
When you hear threatening terms like "Electromagnetic Pulse" (EMP) and the usually Hollywoodesque consequence that everything electrical dies, what you're really hearing about is a powerful enough electromagnetic signal (no different from radio other than the amplitude is overwhelming) that those long wires (like your house wires) suddenly start acting like antennae and channel all that energy into unprotected circuits. Lights, cheap electronics like your clock radio (stuff that's slowly going out of style...) are all examples of unprotected circuits. Your lights are especially a good example. Most of the time they're not a grounded circuit other than to ensure the fixture never energizes if there's a short.
I've actually lived through this kind of an event. A lightning strike occurred close enough to my house to fry phone and electrical wires inside the wall. It coupled energy on the Centex-style parallel cable between my computer and printer. It didn't hurt the protected computer, but it fried the data input board on the printer. Phones died. Lights died. I'm glad to have not suffered worse because my house could have burned down.
In a similar manner, a strong magnetic pulse can damage computer circuitry. More specifically, it can damage memory. Hard drives, some on-board memory types, etc. (Stuff that's slowly going out of style.) A big enough pulse, such as one that can be created with a nuclear explosion, can scramble magnetism-dependent circuitry. To my knowledge, there's not a way to naturally generate a magnetic pulse without the electrical component.
But what's the opposite? I want to damage just the "thinking machines."
Let's assume you're looking to damage the machines and not simply wipe the memories clean. In that case, we're dealing with short wire antennae. Really short wire antennae. As in you're trying to couple energy onto the traces between the major components inside the computer chips. Or at least the data busses inside those chips (the longest wires short of the power and ground planes, which aren't really "wires").
This means the wavelength or frequency of the electromagnetic pulse is important.
Simplifying things a bit, the length of an antenna is 1/4 the wavelength it's expected to deal with. A 100 Khz radio station is broadcasting on a wavelength that's 3km long. The ideal 1/4 wavelength antenna length is therefore 750 meters long. We don't have the time to go into antenna physics here. Suffice it to say that you can use harmonic fractions of the ideal 1/4 wavelength... but now you know why old style AM radio with short antenna had a really limited range or they had a honking tall antenna.
We're talking about picking up a wavelength that's 4X the length of the average bus wire in an integrated circuit. That might - maybe - be as long as 2mm. That's a frequency of 150Ghz. That's in the microwave frequencies.
- And that brings us to problem #1: an EMP capable of coupling energy onto the bus lines of integrated circuits would cook every animal within its range. Including humans. It would vaporize water and shatter trees because of it. There's a price to be paid to do what you're trying to do. Why don't cell phones cook our brains? Well... Ignoring certain realities, the amplitude of the signals isn't anywhere near what's needed to heat water, which is how microwave ovens cook. Let's ignore all this for now.
However, if you did this, your lights would flicker but not be affected. The frequency is too high to efficiently couple energy onto lines as long as your house wires or the cross-country power lines.
- Problem #2: Well, maybe... The physics of coupling energy get a bit funny when you're trying to affect something really small (I have two words for you, just two words: impedance matching). Let's just sweep this under the rug.
When I mentioned cellphones, you might have thought, "if Ghz transmissions are dangerous to computers, why doesn't my cellphone burn itself up?" Remember earlier when I mentioned protected and unprotected circuits? The amplitude of cellphone signals aren't high enough to get past protected circuits.
- Problem #3: You have a real problem here. My computer wasn't damaged directly by the lightning strike because the frequency of the EMP was way too low (we'll ignore the fried surge protector that, had it not been in place, would have damaged the computer's power supply. But that's not damaging the computer per se.) Here's your problem: every pin on every critical integrated circuit is protected with what's called ESD Circuitry. "ESD" means "Electrostatic discharge." Up until now, ESD meant things like picking up the chip without first grounding yourself. You know those little electrical sparks you used to annoy your younger siblings? That kind of thing wreaks royal havoc with electronic circuits. That's ESD — and every pin has circuitry to protect the inner circuits from it. Problem #3 is that a Ghz-level EMP looks an awful lot like ESD. Now, that could work in your favor from a suspension-of-disbelief perspective by suggesting a great enough amplitude that the ESD circuity burned out, effectively disconnecting the pins from the internal circuitry. Of course everyone's BBQ, but let's ignore all of this, too.
OK... so what's the real problem? Bring on Problem #4 already!
- Problem #4: Everything's a "thinking machine" today.
You're 30 years out of date in the way you're thinking. LED lights have control circuitry that's nothing more than simple integrated circuits. Any natural EMP that could hurt a computer would hurt the computer in your LED lights. And your cell phone. And your car. And your washing machine. And your refrigerator.
Problem #4 if that you're too late. Even if we come up with a believable natural event that could damage short-wire computers and not long-wire house circuitry, all that long-wire house circuitry powers short-wire computers. Many electric razors have integrated circuits inside them. Everything would burn up. Instant 1968.
But you won't mind because you're BBQ anyway.
But let's ignore all that.
What natural phenomena could produce a 150Ghz pulse with enough amplitude to couple energy onto a significant number of computer chips, frying them like so much dough in hot oil?
To be honest, I don't know of one. Even a nuclear blast is slow compared to what you need. I'm sure I don't have a complete meteorological knowledge to judge what conditions could exist, but everything else I can think of (electrically charging the atmosphere, raising the ground plane voltage in the soil, solar emissions of any kind...) simply can't produce the nasty mess you need to
cook humans damage computers.
A fast enough lightning strike could do it, but (a) it must strike someplace where the energy can dissipate really quickly, like the middle of a lake where there aren't any computers to blow and (b) lightning has a very limited range. A bolt with enough energy to affect a really wide area would require a lake of exactly the right salinity and purity to dissipate the energy while it's vaporizing. Water really isn't a great conductor.
Gratefully, you're using the science-fiction tag
At the low end of suspension-of-disbelief is the idea of a super-lightning storm that produces strikes that achieve what you need.
Middle-of-the-road suspension-of-disbelief would be a condition that causes very powerful ball lightning using something along the lines of the proposed Microwave cavity hypothesis. This could conceivably produce a magnetic pulse (vs. an EMP). Remember, magnetic memory is disappearing. You'll probably see that in your lifetime. And the result would only be scrambled memory, not damaged computers. But, hey... it's something.
Also in the middle are solar events like flares or mass ejections. This stuff wreaks havoc with satellites, but very rarely affects the Earth. When it does, it tends to affect long power lines (antennae...) and not computers. But SciFi has been blaming solar flares for everything for a long time, so your readers won't notice.
At the high end of suspension-of-disbelief is an atmospheric meteor strike that produces an EMP equivalent to an atmospheric nuclear blast but for whatever reason (maybe it's not dense enough), it doesn't hit the ground causing an extinction-level event.