Computer "restarts" randomly

My computer has been restarting once each boot-up, and then randomly restarts
approximately once an hour, without any apparent precipitatng cause.
It may restart when the computer is sitting or when I close a page or start
a program, or it may happen while I'm typing this message. It always
restarts and the scanDisc screen (blue screen) comes up. I shut off the
"turn off the monitor" function, but doesn't matter. I'm concerned that this
is pointing to a weakness in power-management or hard drive. It doesn't seem
to require a heating up of the power supply, but maybe the power supply is
going bad. Anyway to check that? Maybe the memory card is loose. Any
suggestion of what to look for?
thanks. Ron