what is wrong with my amp and cap?

It was not visually blown as a fuse normally is, it was broken, so your telling me that the AGU gold plated fuse does not blow so you can see it thru the window, that when it blows the solder joint breaks,,,,,c'mon, I must be mis-understanding what you said.

That should be just fine, but it brings up another question?

Where were you getting the remote turn on for the amp that was always working?  i'd think that you would get the remote turn on lead from both amps at the same place?

A gold plated AGU fuse will blow if you pull too much current through the fuse.  If you are pulling 50 amps through an 80 amp fuse for a long period of time, heat will build up in the fuse and the solder will melt off of the element.

Well just as a precaution, you should find where the remote leads are coming from!  There has to be a reason that the kicker remote turn on quit working, and the Alpine didn't.  If it was hooked to the remote turn on from the deck then your remote turn on output just went out.....if it was hooked to an accy or ignition wire from the actual vehicle then something else went out in your vehicle.  I'd check just to make sure nothing else crapped out.  Also, if the Alpine's remote turn on lead IS hooked up to an accy/ignition wire from the vehicle, make sure that it is fused to prevent possible problems in the future. 

Not to difficult to do, but could save you some headaches down the road!