HP Problem: PC going into "Sleep Mode"

[EnFoRcEr!!]

Well, my wifes friend brought over her pc saying that it would shut off by itself, kind of like it goes into sleep mode. So I decided to try it myself. She has an HP Pavilion 513c. Onboard everything(uses seperate card for LAN though. So anyways, I boot the computer up normally 2 or 3 times, and it does it off the bat. The computer basically goes into sleep mode, with nothing running but the harddrive. The only problem however is that you cannot recover the PC without restarting it manually(power button). I then tried to run it in safemode, in which I booted successfully a couple of times(although it was a pain getting the USB stuff to boot, lol). However, when I went to shutdown the pc again to reboot with networking enabled, the problem happened again. So I manually restarted, and it did this 2 more times...once again in Safemode, and then in regular boot-up mode.

It doesn't seem to be a problem with anything like overheating because I've checked it myself, and it is far from hot(not to mention it is too random. Sometimes it happens before you ever see the login screen, other times not until 10 minutes after you login). Although, the only time I was able to successfully login were in safemode. I'm also sure it isn't a video deal or any type of driver, as it has happened both prior to windows loaded, and while it was shutting down. I'm thinking it could be a memory problem possibly, because we all know how tricky they can be. Unfortunately the ONE TIME in my life I do not have a floppy on hand to run a memory test is today, lol. Other than a memory issue though(or POSSIBLY the harddrive), what do you think could be causing this?

I've seen pc's shutdown on their own and do lots of wierd things, but this is a first for me with sleepmode being activated.

 

[EnFoRcEr!!]

Also, I should problem mention that I checked for any odd or incorrectly set Power Settings, and there were none.