Processor fan problem (please help!)

I have been having a problem with my processor fan lately. When I turn my computer off, which is not that often, and sometime later turn it back on, the processor fan will not spin. The system will power up, the CD-ROM drive lites blink and so does the one for my Zip drive, and I can hear the hard drive spin up. But then that is it. After a while, the monitor will go into Power Saving mode, so it itn't getting a signal when it does this. To turn it off, I have to hold the power button for several seconds, and when it turns off, the fan will spin slightly. The only hardware I have changed was, I added a 16mb stick of ram, and a ATI Rage II+ video card. I can ususally get it to work after turning the computer off, but I have to turn the computer on and off rapidly before it will spin up. I turn it on, but hold the bower button down, and several seconds later it turns off, anf then as soon as it turns off I turn it on again. I keep doing this untill I can feel air hit my other hand, behind the computer from the processor fan. I don't want to keep doing this because it is probably bad for the computer, so I have just been leaving it on lately. I will probably have to replace the fan, but I wanted to ask here first
My system configuration is:

Dell Dimension XPS D233, service tag CP3GT
Intel Pentium II processor @ 233MHz, overclocked to 252 in Windows w/ SoftFSB
80Mb ram, upgraded from 64
STB Velocity 128 4MB ram in AGP slot, mostly unused
ATI Rage II+ 4MB ram w/ TV tuner and PC>TV capability, primarially used card in PCI slot
Motorola VoiceSURFR 56K Internal, ISA
Creative AWE64 Sound Blaster, ISA
Standard CD-ROM drive included w/ computer
Hewlett Packard CD-Writer Plus 9300
Iomega Zip drive Internal, but not hooked up, except for power