My 1993 Jaguar XJ6 has started to shut down the radio and air conditioner. It happens when the weather is very hot and humid. The weather was cool this week and it worked ok for awhile but when it sat in the sun it started again.
I would check for a bad connection in the power line to thoses areas. They are most likely fed from the same main fuse so check the wires connections to that also.
You should consider investing in a service manual to help with this. The money you save from a shop repair will pay for the manual. Having the manual will save you time too.