If you wish you can replace the visibly burned components in the power supply, and it
might make the unit work.
We can assume those components burned prior to the fuse blowing. It's possible they were the root cause, nevertheless it's equally likely they failed because of a component elsewhere. Not necessarily a short circuit, but something bad happened yet it didn't blow a fuse right away. That may be a clue of some sort. Any unusual event at the moment of failure is a clue.
when you say output devices are you referring to the speakers, if so how can these be tested?
I meant a transistor array or IC which drives each channel.
Good quality hi-fi usually has tweeter, woofer, sometimes midrange. Therefore several output devices.
It could all be contained in a module to serve all the speakers. Look for a block of metal with fins exposed to carry away heat.
Is there a chance the output module was overdriven? Not that I know anything. In fact there's nothing wrong with going ahead with what you intended to do, since it's a few inexpensive components. It may be sufficient, although more diagnostic testing is wise before you apply full voltage to the unit. Such tests require knowledge of the circuitry, points to connect power, points to feed audio, etc.
As for buying from Ebay, sellers in your own country often offer free shipping on small items. (Can we bargain hunters resist even if it's a depot distributing Chinese products?) To play it safe, bid only to sellers who have better than 96 percent positive feedback.