It does sound like you have a board/hardware problem, going by the results of your pretty logical testing. Especially as both internal and external floppies are effected.
Have you tried your friends psu on your amiga? Maybe theres a problem with one of the power rails...?
The temperature of the chips is not always a sign of a problem to be honest, unless it gets to the point that you can't keep your finger on it for more than a second or two, which is usually too hot.. ;o)
However, as stated it does sound likely to be a board fault. Not much you can diagnose/repair yourself with surface mounted stuff (unless you have the expensive gear to hand?). Probably not worth trying to get it repaired either with so many 2nd hand ones popping up these days for so little....
(
Hope thats of some help?
