Replace existing PSU fan with a panaflo, papst, etc. low-noise 80m fan. Hook it up at 5V.
Then just get a large enough heatsink, which by today's standard can be pretty small. It's a Pentium 233! I just took one apart a few months ago, the heatsink was like a 8mm slab of aluminum with some thick fins that pointed up like 4mm. It was coupled with a tiny fan that hardly moved any air. It was clogged with dust when i took it apart too, no stability problems though.
Air flow and fan noise isn't going to be the issue though for the system. It's going to be vibration! First from any fans, but using isolators fixes that, then from the drives.
What kind of hard drive are you using? My parents are still using 3GB, 1.6GB, and 1GB hard drives in their computer. The 3GB Fujitsu one is REALLY loud. Louder then everything else, the loudest fan in their system is a 12V Panaflo L1A, and the drive completely drowns that out.
To quiet the drive your going to need to decouple it, or maybe even isolating it in an enclosure.
To cut down on remaining noise, look into sound absorbtion materials to line the case with. Melamine Sound Absorbing Ceiling Tiles are inexpensive and work, you can get some at
www.mcmaster-carr.com
To get more suggestions and help, I think you should read the articles at
SilentPCReview, and then post in their forums for help. They'll know a lot more about silencing computers then at other computer forums.