I have an amp that used to do that too(not an alpine though).
I sprinkled a bit of heat (with a hot air gun or solder station)about the place while it was turning on and found that when I heated up the really big caps in the middle of the amp board, it very quickly started running. I then replaced these caps, and just about every other electro for the hell of it as the amp is older than 25 years.
No more problems since!