Amiga 500 issues.

[Lurch]

I'd try re-seating all the chips, most likely one is not sitting right.

You could start by pushing each chip to make sure they're inserted okay.

Is it a 500 or a 500 plus? If it's a plus it could be the onboard battery causing problems, I'd remove it. Once removed you can clean the area with lemon juice, but make sure to remove all lemon juice after you finished and make sure it's dry.

The lemon juice stops the battery acid from doing further damage.

The other thing to check is if it's got an expansion card that too has a battery onboard, same deal remove it and clean it.

As for the floppy drive you can try cleaning it with cleaning alcohol and a cotton bud but most likely the drive might be out of a alignment.

This is a good article

http://www.techrepublic.com/article/quick-steps-to-service-a-broken-floppy-drive/1055927

If not Amigakit sell new drives...

http://amigakit.leamancomputing.com/catalog/product_info.php?products_id=106

Although Floppy drives are a real pain, so I've switched to an HxC2001 floppy emulator

http://hxc2001.free.fr/floppy_drive_emulator/

[Lurch]

You can open up the external drive and use that, although it may not align properly with the button on the side.

But give it a try.