What board will fit in this case....

That's a small form factor case, which means there isn't really a defined standard. We'll just say "something smaller than microATX" most likely.

You'd be better off buying a new case. It will cost you more to buy the tiny parts you'll need to put in that case, and you won't have the nice expansion room, air flow, or big choice of parts.

The board and PSU are almost the whole computer. The rest of the components in the case can be reused in any case. I'm looking at you, hard drive, floppy drive, RAM, CPU...

I can try to help you out. What kind of RAM and CPU do you have? Can you measure the spaces available for each? I'd say an SFX power supply will probably fit, unfortunately, it's pretty difficult to find a decent-quality one of those.

Measure the outside, for the coffin. This is archaic technology. It's so old I'm not sure where you'd find anything to fit. It might be "baby-AT," which no-one makes any more, and isn't even on Newegg's form factor dropdown. The floppy might be salvagable (if you really need it). I'm not sure I'd trust a HDD as old as that one, but maybe you could put it in an external USB enclosure. Sorry, but I think you'd be wasting time and money to try and make anything significant out of this.

I get old machines all the time that people give away or cost 5 bucks at a sale monitors ,keyboards, mice you name it.Some of them actually still work.A friend of mine left an old compaq on my doorstep which he said he couldn't get to work and after cleaning gobs of dust out and reinstalling windows it runs like a champ.Other than that with my spare parts from other machines I can get most things running.My point is you can get a machine that is just as good or better for nothing nowadays so why spend any cash?