" good images from our DVD player?"
Hmm, it’s tricky without seeing the actual setup.
Nooooooobody expects the Spanish Inquistion!
I think it’s a dirty tape, too. (No, not that kind of dirty tape) 
If you play a tape that has had something spilled on it (like soda), it will gum up the spinning head within the VCR, causing a loss of picture (and the ability to record). Later, when you play a ‘clean’ tape through the machine, the crud will gradually wear off the head and restore the heads ability to read/write. Sometimes this take hours.
Would sunshine do it? You know sun hitting those precious video cassettes & softening them up a bit…hmmm. Our local Longs asks us not to keep them in the sun.
Looks like dust was the problem. We bought a VCR cleaner and cleaned all our VCRs and tried out one of them in the bedroom. Worked fine. Still working fine. I also put some small sponges at the corners of the VCR so it’s not resting on nothing nohow, to prevent overheating.
I’ll come back and whine some more if the problem recurs. In the meantime, thanks for all the helpful suggestions.
Man, this just makes my day! Several people make other suggestions, then I come along with my not-quite-WAG (I did work in video production for many years), and I get it right! Hooo-boy!
I hope this proves to a few Dopers that I’m not just a lame-ass, persnickety, arrogant, stuck-up dilletante.
I’m a lame-ass, persnickety, arrogant, stuck-up dilletante who can be right at least once every 150 posts or so.