For the record, my friend had the exact same problem in a Glant VR-4, and he found that when his car was running and he turned the wheel that the belt on the pump was slipping. You could see the pulley on the pump physically stop turning for a split second. Tightened his belt and it stopped.

I have the same problem with my '90 laser (which is a donor car for another chassis), and I'd spend time diagnosing it, but the ECU fried last week and it's not going anywhere until I gut it. 'don't need power steering in the Colt which has a manual rack already... so...

Hope it's something simple. Get someone to watch the pump while you honk the wheel left-right. Could just be a glazed belt.