Does it have to be a suppression field or is any effort by aliens to screw up computer tech ok?
Computer chips are difficult and expensive to make. Chip fabs cost billions to build. They're also easily contaminated. Quantities of copper vapor too low to quickly detect with the best instruments can be enough to destroy chips partially through fabrication.
So what if instead of trying to violate/suppress the laws of physics the aliens simply released swarms of little nanobots which attempt to contaminate any high tech production facilities and sabotage any working high tech devices?
If they encounter a chip fab or something that might be a chip fab they crawl into the machines and release metal dusts of many elements and/or gum up the works any way they can.
More clunky, bulky technology is mostly unaffected while the more precise and delicate the device the more easily destroyed.
If they encounter something that may be a computer they try to lay down metal whiskers across junctions to short circuit them.
Computer chips work for a little while if you're lucky but sooner or later some of these bots burrow into them and kill them.
This would pretty much destroy the computer industry. Some organizations might be able to build small scale fabs in sealed locations and keep a small number of machines running but it would mean almost zero computers in everyday life.
The effects on health would then be easier to guess. Lots of nanobots would probably be bad for your health, especially breathing them in. It could even make being around high-tech devices hazardous for humans if they swarm towards them.