Some general questions to help us narrow down the possibilities:
1. Can you give us any more specific, exact information about the Memory problem error? If the computer had stopped responding, how were you able to run the check up, and exactly what "check up" program did you use?
2. When did this start happening? Had you changed/added/removed any hardware or software around the time you first saw the problem?
3. Does the problem happen when you boot Windows into Safe Mode? You can get to the Safe Mode start-up option by hitting the F8 key just as your computer is starting up.
4. If you just let the computer sit for a while after it boots, will it eventually begin to function correctly, or does it stay "frozen" indefinitely?
5. Tell us exactly what version of Windows you have, and give us the specifications of the computer's hardware.
6. Disconnect any external hardware (printer, USB devices, network cable, etc.). Does the problem still occur after doing that?