Dimension Desktop will not start -- until CD drive drawer opened

I have a Dell Dimension 9150, running Windows XP. Suddenly today it failed to boot. It would power on, show various LED indicators, show one CD-drive light, then the other, run the  fan at high speed (it normally does this at boot-up), then turn off. Screen remains blank. After a few seconds it would repeat the process. Eventually, I stopped it by holding down the power button. Strangely, I found that if I pressed the button on one of the CD drives at the right moment, the tray (both drives are empty -- there is no CD in either  tray) would open and the PC would boot normally into Windows. This behaviour has continued -- I can only boot normally by opening the empty CD tray a second or two after turning on.

Any ideas?