Finding units wit working drives maybe a bit problematic. A quick check of E-bay indicates the disc loading/reading issue may be common.
An approach I would take:
First get the manuals for it:
http://www.digitalfaq.com/forum/vcr-...0-service.html
Looking at the schematic it looks as if the unit used either a JVC DVD burner (in USA) or Hitachi-LG DVD burner (in a European variant).
Carefully remove the existing drive and its covers to see what is going on inside.
If I could identify the drive, I would try find a drive of same make and nominal capability from the same time frame.
It shows 40-pin IDE/ATA interface, probably ribbon cable rather than the external cables used in a PC. This should map pin-for-pin to the standard ATA connector used in a PC drive.
However, the power to the drive appears to be either 4 or 7 pins (7 for US, 4 for Europe). The purpose of the other three pins in the US is not clear to me. Removing the cover might shed more light on this. But it should be resolved. By doing a side-by-side comparison of the existing and proposed replacement drive you may be able to sort that out. If all it does is light LEDs or similar it may not be needed.
If you do install a different make/model drive, do not try to flash its firmware with the JVC.