A good clean is always a good thing to do. But do it with the mains lead in, but switched off at the mains end (so that the PC is still earthed)
I always use a vacuum cleaner with a soft head - but many people say you shouldn't, you should use a can of 'air' to blow the dirt away.
Once cleaned, try re-setting the power supply.
Switch off at the rear. Pull the power cord. Press the power button on the front of the PC for 30 seconds or so to discharge any residual power held in capacitors.
Turn on at the mains. Plug the power lead back in. You should hear a faint pop as the PSU absorbs the power. Switch on at the rear and then at the front in the normal way.
If you originally removed the floppy drive with the mains attached and powered up - there is a small chance you may have damaged something. Modern PSU's and mobo's are never powered down by the front switch. You can often verify this fact by the noting that the network connection LED's are still on when the PC is supposedly off.
When working on a PC - I always switch off at the mains, but leave it plugged in to maintain an earth connection.