First if your amp is blowing fuses upon power up, DO NOT go to a larger fuse, you have a problem either with wiring or the amp itself. If you blow a fuse when the amp turns on, your amp could be bad. And if the amp is bad, placing a larger fuse can cause more damage to the amp. Amps blow fuses in this situation if the power supply has been damaged or you have a bad output device in the amp.
I would suspect the amp is bad because you can't have a short only when the car runs (unless your main power lead is not coming from the battery and energizes only with the car on, which is very bad)
All radios should put out 12V to the remote/power antenna lead. If its not, your radio has a problem or you were wiring it wrong.