Probably best to start at the floppy. Does it make any noise or does the FDD light come on at all?

Might have to pop the system open to check it all out.

Sounds like it's not dead, maybe just dirty?  Wouldn't be the first floppy drive to fail, though.  You could also try swapping the drives between the two for testing since they're compatible.

Sure, that's what they give you with the head cleaning diskettes as well.

Those head cleaner floppies always worked well for me, but you can also use a q-tip with alcohol on the heads (never tried this on a 3.5" drive though, could be tricky.)

I've even gotten away with wetting an old floppy with alcohol and running it for a few seconds when nothing else was an option.