I'd agree with Andy, it sounds like the power supply is struggling.
If you are trying to mend it yourself then disconnect the tower completely from the mains, open up the case and try disconnecting the cd drives power cables to reduce the start up power.
While you've got the case apart give it a quick dust off, try to avoid using the vacuum cleaner though as the static can damage your PC.
Put the case back on and power it up.
If it starts ok without the cd drives then buy a new power supply.
jim, May 2009