I am in a school environment. Is there a way to run a VCR into a desktop so as to use a digital projector (ceiling mounted) to display VCR movies? I am aware the VCR can be plugged directly into the projector but since it is ceiling mounted in the middle of a large room I just thought it would be easier if there is a way to simply run it through the computer.

It wouldn't be very easy, and it definitely wouldn't be free. A VCR outputs either an RF-modulated signal or a baseband audio and video signal. You would either require a tuner card for the RF signal, or a frame capture card for the video. The sound could be fed into the audio inputs that are pretty common so that's not a problem. You would also need a program to convert the audio/video to something that's displayed on the computer screen so it could be routed to the projector.