Not having the right power supply could definitely cause this type of behavior. If the system can not get enough power when it needs it several different systems can produce errors. Usually the CPU. It would make sense, at boot it requires more power as every component is initializing.

I would wait for the correct power supply and reinstall the OS at that time.

This could also be a hard drive error or memory error. If you are able, download the Ultimate Boot CD and burn it to a cd.
Then if you are still having issues after the new power supply arrives, boot this CD and run Memtest86 and a Hard Disk Diagnostic Tool.
(ultimate boot cd can be downloaded here from the right ---> column, under free downloads)

More info can be found here.
Ultimate Boot CD - Overview