Monitor keeps going to sleep, even after buying a new computer.

Hello, my problem is that my monitor keeps going to sleep right while I'm working on the computer. The repair guy said that my video card is going bad and replaced it. That did not fix the problem. So he said it was the power supply. Replaced that with something more powerful and then it got worse. So then it just quite working all together. He said that my motherboard went bad. So he built me a computer. The only parts he reused was the new power supply and my dvd maker. He replaced the Hard Drive,
Motherboard, Processor and Ram/ Memory Bundle, Case w/ 3 fans included .

The only option to wake the monitor up is to unplug the computer and plug it back in. I have done this 5 times today alone. I use this computer for business and it's frustrating to lose your work.

I do notice that it shuts down more when the Internet is up. I previously ran Firefox browser. Today I uninstalled that and installed Google Chrome. And it still shut down all those times on me. We never play games on this. When I received the new computer back it worked fine for a few days. Carbonite has been restoring files on it for the past few days. Could a virus, malware or some other vicious spyware be causing this problem?

Any suggestions or solutions to fix the problem will be greatly appreciated.