If it's the tape itself that has snapped, I've actually repaired VCR tapes by putting the two broken pieces together with plain old adhesive tape (make sure the tape isn't twisted). Take care that the adhesive tape is not wider than the video tape (trim with nail or other tiny scissors) and that it lays very flat, don't fold it over. Use a single, very small piece of tape on each side. You will have a very brief skip in the tape, but it should work fine for quite a while longer. And you can always do the same thing next time it breaks, as they tend to break at the same spot later. Good luck.
Shari