It should only take a minute or so, and Amigas should be just as fussy as any other DD disks (not as bad as recycling old HD disks).
If you take the floppy out you can carefully pop the top off (they click together, it's easy to figure out how to take 'em apart, but the metal is easy to bend by accident!). With the top off you can check for fluff etc, but again it's easy to mess up the internals by accident.
If the problem is alignment or a broken head it will be time for a new drive. If you tried several disks that look ok on the outside (and under the shutter) then it probably isn't them, unless someone else threw them out of course ;-) Like Matt said, it's worth checking the cable & clearance, but if you've not been in the case already it's unlikely.
