I just set up one of my IIe's on my desk. I have it sitting under my 20" Dell LCD, which has a composite input, and setup a serial connection (Keyspan PDA Serial-USB adapter) to my G4. I haven't messed with the Apple II game server yet, but I got ADT Pro working.

I have some known working disks and drives, so I could test both your floppy drive and disk to see which is bad. I don't know much about fixing a bad drive however.