Indeed, the first thing to try is cleaning the heads. If memory serves the head gap is <14 microns so they clog very easily and will often cause a no picture condition.
HOWEVER - you must be very careful or you will snap a head off. If you do that (or it's already been done), throw the unit in the trash.
First locate the video heads which are in small openings at the bottom edge of the head drum (the silver rotating drum with etched groves). There can be two (180 degrees apart) or four (90 degrees apart).
The correct way to clean them is with a small piece of chamois dipped in alcohol (methanol is best but isopropyl is Ok). You must only wipe in the same path the tape would travel - NEVER up and down. Use the etched groves as your guide, gently wiping parallel to them. The chamois is used because cloth will snag and/or leave lint.
If you've never done this before it might be best to view the heads through a loupe first. That way you'll know what the head looks like before you start wiping. Also, if it's already broken you'll see that too - instead of blaming yourself. The actual heads are usually about 3/16" long and about as thick as a sliver of mica. The gap is in the middle of the head - that's what clogs.
Like wagon mentioned, some units will mute the signal below a certain threshold (like some TV's show a blue screen when there is no signal). Therefore you may not see snow with a clogged head.
Be sure to clean the audio/control/erase heads while you're in there. They're in the housing that resembles a normal audio tape recorder head. No worries there - just wipe away.
Good luck.