Is it the VCR, the antenna or the TV set?

The VCR on my VCR/DVD-player can no longer play videocasettes (yes, some of us still use 'em) or record off the TV screen. I got out my old VCR (the one I had before I bought the DVD/VCR combo), which was still working before I retired it, hooked that up to the TV, and found that the old VCR wouldn't play or record either. I read where the heads might need cleaning so I did that and both VCRs still wouldn't work, It seems odd that both VCRs would be broken, so I thought it might be the set. However, the DVD part of the DVD/VCR combo works just fine hooked up to the set. I notice that some of the tv stations I've had no problems viewing are now coming in crummy, and adjusting the antenna (I don't have cable and use "rabbit ears") doesn't clear things up. It seems too unlikely that the antenna has gone on the fritz just coincidentally the same time as the VCRs. Is it possible the problem with the VCRs is in the antenna? I'd hate to buy a third VCR and find that it doesn't work, either.