Wow thats a classic setup.To me it looks like a Matsushita/Panasonic clone or a Hitachi clone made VCR and Tuner.I could be wrong since it was 30 plus years ago when these came out..Camera is more likely a Panasonic clone since its using a Newvicon tube patented and made by Matsushita.
I think I have a similar setup here somewhere.
The battery is more likely shot.I would check the caps and for burnt parts and bad fuses in the tuner and the VCR power supplies.
I'm wondering how crisp is the image on the camera and any burn marks on the pickup tube from aiming it at bright lights.
I found this with Google image search using "rca portable vcr and tuner"
in the image search.
http://blog.cyborg5.com/?p=87
Your could be the RCA VFP-170 setup if I read the article right.