I agree that it sounds like the power supply. I would try disconnecting anything you don't actually need, as you said without the floppy drive it worked better. So disconnect the optical drives and spare data hard drives, if any. If it works better yet again, that's more evidence towards the power supply being unable to handle what it once could. Still, it might be something else and that would be real hard to determine for certain without replacing the power supply and seeing if your troubles go away.