Honda Civic - Radio/Dashboard Issues

My wife's car is a '98 Honda Civic EX. She no longer has the factory radio installed in the car (it was replaced a while back). Just recently she had the timing belt replaced along with some additional tuneup work. Over the past few months we have noticed that on occasion when tapping the brake pedal, the power to the radio and sometimes entire dashboard will go out for about a second. At first I thought it might just be a radio issue, but since it is affecting the whole dashboard now I'm curious as to what the problem is. The place where will got the tuneup won't claim responsibility for it and the place that replaced the radio (Best Buy) says that it's a problem with the vehicle.

Any ideas/suggestions as to what the problem might be?

Thanks.