alpine stereo problems, 94 saturn

Ive got a problem with my car stereo and i was wondering if any of you electronic whizzes can help me. I have an Alpine that i installed into my 94 saturn, and before i installed it, the factory radio would always lock up and just shut off. Once i installed my alpine, it did the same thing. This was last winter, and when summer came around the problems stopped, and my radio always worked fine. As the weather got colder this fall, the problems started happening once again. As of now the radio completely doesn't work, and won't even turn on. Also if this helps, before the radio shut off completely, when i would tap my brakes, the radio would shut off, and the also if the head lights were on, they would dim. Wierd i know, but saturns are known for electrical problems, and i just want to know whats wrong with it, any suggestions?

thanks!