I had a problem like that along with another issue with my computer. Mine at first, the screen would flicker or blink once and reboot and tell me that windows didn't start properly and give me the option of starting in safe mode. Eventually it got to where I would hear a clicking sound in my computer, about 3 clicks, and then it would turn off. Then it would be hard for me to get it to start back up. I would have to hold the start button in for 8 seconds or so until the green light to the left of the button turned off, then press the start button again. Sometimes I would have to go through that for 5 times to get it to start back up. I asked someone about it and was told to suspect my power supply. I bought one for $30 and put it in and that took care of the turning off problem and getting it to start. But there is still an issue with rebooting. If I take out either one of the two 512mb memory modules everything is fine.
Mark