If a drive can't even read a known-good floppy that it formatted, it sure sounds like a drive problem. The first thing to try, as you suspected, is to give the heads a good clean. These drives can also suffer a form of arthritis, in which the lubricant gradually turns into a glue-like substance. That can prevent the heads from loading properly onto the disk surface. If loading/ejection seems a bit balky, a good clean and re-lube is probably a good idea.