Just a shot here, but ya never know:

I once bought a (REAL) cheap equalizer / power amp for my car tape player 
at one of those motel-room truckload sales, and it sounded great.  For a 
while, that is.  Then one channel quit entirely.  I opened it up, and the 
amplifier chip for the bad channel had simply melted some of its solder 
joints attaching it to the PCB.  I soldered them back and it worked fine.  
I just had to keep the volume a bit lower than I did before.  Probably 
lousy heat sinking.

You said "a nice Alpine" which I'm sure is a few orders of mag higher
in quality than the P.O.S. I had.  But the point is - look inside before
you scrap it, since you OCCASIONALLY find something you can repair.
Maybe even the same thing I found.