There are no digital/analog issues, because the video signal coming out of your VCR is analog, just like the input on the projector. I'm assuming you're using the composite (yellow RCA connector) connections, right?
I use portable projectors all the time at work, and someone is always changing the input device setting. Our projectors can be hooked to two seperate VGA connections plus an RCA composite video connection, and there's a button to switch between the three inputs. See if you have something like that on your projector.
Also, if you have a DVD player, you might try hooking THAT up to your projector as a double-check. Right now, too many things could be wrong. Bad cables are always the primary suspect after you've ensured the correct settings on each of the devices.
-Troy