For some reason, both of the new (refurbished) computers that I bought seem to go into a sleep mode after about 5-10 minutes of being on. I am guessing this because the monitor light turns orange instead of green, and the display goes away. Until I got my 3rd computer, I wan't able to test if the computer was in safe mode because the 2nd computer was too old. This 3rd one's light near the power button continuously blinks when the monitor's display turns off. This is why I am guessing it is in sleep mode. I know that processes on the computers are still working though. Is this safe mode or some other kind of a problem?

PS. The monitor I'm doing this with has worked perfectly fine for a few years with the computer I am currently using.

Maybe.  Processes will work when the computer is in sleep mode, but internet connections tend to die.  Try connecting one computer to another on a simple socket and see if it's closed off when the computer...sleeps.

Go to Control Panel > Power Settings [or somethnig like that] there should be some options for turning on/off stuff like that.

Thanks for the help guys. I went to the Power area under Control Panel but it didn't have anything to control the kind of power I was looking for. The computer was Windows 95, so that could have been a problem. Anyways, I upgraded it to Windows 2000 Pro and so far it works fine. I took off all sleep mode settings, it was at default set to go into sleep at 20 minutes.