I got an A500 with the same sumphoms... though I guess mine might be a bit worse since the drive will only see inserted disks about 50% of the time and then only spin up the drive motor for about like a sek tops and then stop...
I'd probably look at the drive, first. There are two little sensor switches in most Amiga drives. One senses write-protect, and the other is simply disk inserted. If those are overly dirty or worn down, the Amiga won't always "realize" you inserted a disk (or will think all disks are write-protected). Doesn't explain the reading problems, though. Drive may be toast.
Of course, if you have other CIA chips sitting around, swapping them out wouldn't hurt the testing process, either.
Also, I forgot to mention one more. Damaged / loose ribbon cable from the floppy drive to the motherboard. Can also cause same symptoms.
