You have to do some trouble shooting.
You said you tried multiple VCR's and multiple tapes. That pretty much rules both out as being the problem source. That leaves the cable and the speakers.
When you plug in the speakers is it always the same one that doesn't play?
Try reversing the left and right connections into the VCR. Which ever speaker was playing, now should go off and the other speaker should work.
If the same speaker as before still doesn't work, that speaker is suspect.
If both speakers pass that test, then the cable is the most likely suspect.
In that case:
Test the cable with some other source if you can, like a working CD player or cassette deck that has the same kind of left and right audio outs as the VCR. Connect the Y cable, play a stereo source, and if one speaker still fails, it's probably the cable.
Are you sure that you have a proper stereo adapter cable. There are similar looking Y cables meant to split a mono signal into left and right and they would not work.