I have an answer for both shutting off and interference:
The conditions in your storms are different from ours, what that cause is will be up to you however the hand waving for interference could well be one of cloud makeup; either chemical (not just water vapor), or perhaps the dust and debris that humidity condensates onto in the upper atmosphere (for your world this dust could be metallic in origin, etc.)
In response to your comment on the nature of the unique atmospheric conditions: I can see a variety of potential issues that could have triggered these new storms, these may vary based on your worlds history of course.
- Fossil fuels are depleted, many synthetic fuels are created and tested, these leave strange chemical residue in the atmosphere. These new molecules act like tiny radio transmitters when statically charged.
- Based on my thought that it could be large amounts of metallic dust. This could be suspended in the air via unusual geo-magnetic patterns. Or chemically (Note I'm not a chemist =P) Dihydrogen-Copper molecules were created as a bi-byproduct of industry or as you mention alien origin (meteorites?).
The nature of these clouds produces a lot of wide-band radio noise, effectively blanketing the radio spectrum with static interference. Lightning could also trigger strong bursts of radio noise followed by thunder shock waves that "jostle" the clouds and create additional radio noise.
You say the world is similar to ours but in the near future. Have they depleted the worlds oil reserves? Did they switch to nuclear power? Solar? Wind? Depending on your world's main power option the power grids capacity may have to be reduced during storms which would necessitate many (not necessarily all) devices being shut off.
Wind is an easy example here. Turbines on large scale wind generators can only spin so fast with out damaging the blades. If the storms are severe enough heavy wind, rain, lightning; it could be that a storm would require wind and solar generation to be switched into "safe mode."