By computer sounds do you mean the sound of fans and hard drives spinning? If there are no loud distinct beeps indicating a startup error (See Post Beep Codes), then I would check the following.

I'm assuming you mean the power light on the monitor is on. If that is the case then it is one of two things.

1. The monitor is not set to the correct input source.
• Make sure you go through the monitors menu and select the input. Example
  
2. The video cable to the monitor has a bad connection.
• Make sure the cable is connected properly
• If repositioning the cable differently restores the image than the cable is most likely failing. Try replacing the cable with known good one.
• If the cable is good it could be a problem in the jack on the monitor or the computer.
  To repair this would require disassembling the monitor or computer and replacing the jack.
  However, most computers and monitor have more than one type video input/output. Try the other input/output jacks. Example