a 7812 is a 12v positive voltage regulator. It regulates the +12 to exactly +12v. I'll get to it here in a second....
Ok, so, did you recap the amp board, and reflow the solder on it? especially the headers and the amps themselves - those can make it hum, and badly.
The reasoning on the 7812 is this (and it helps to see what the 12v DC looks like coming off of a switcher). The switcher takes an AC waveform (which is a sine wave), then using capacitors and switching transistors clips it into what should be a true DC voltage, with no wiggles whatsoever. However, if you look at it on a scope, you'd most likely see some voltage variation, not much, but enough for the amp to see that voltage fluctuation as a hum. If you looked at the waveform on an O'scope, the AC on top of the DC would be fairly small - like probably less than 1/4 volt, depending on the quality of the switcher, much less. So, if your +12v is running 12.6v, but has ac on it so that its actually varying between 12.35, and 12.85 (or thereabouts, it really depends on how your voltmeter handles dc measurements). The 7812 clips off the voltage at exactly 12v, and gives a nice smooth DC voltage, and gets rid of the AC ripple (in theory at least - i'm not an EE, but i know its helped someone in the past, and thats my theory of why).
Anyway, the noise supressor that i posted the link to does basicly the same thing, but in a different way. It allows the ac ripple to be passed off to ground or filled in with stored energy.
Rat shack most likely will have a 7812 in stock. Here's a link -
http://www.radioshack.com/product/index.jsp?productId=2062600
Anyway, hooking it up is simple - there's 3 leads. Solder wires to each. Ground (ties to logic gnd on the switcher), your 12vish input (+12 on the switcher) , and your 12v exact out (ties to the +12v lead you removed from the switcher).
Edit - there's really no need to replace the amp board. If you have all the sounds, its not bad, but most likely just needs recapping, and chances are, even if you buy one, you may need to recap it as well.
Further - remember that even if you have a good power supply board, you may have to replace the big caps in the suitcase (as well as the bridge rectifier) before you get a working original power supply - and those 55k and 100k caps aren't cheap.