What are the specifications of your old PC? On older machines, fans can sometimes simply be replaced by good quality heatsinks hence eliminating all fan noise.

As William said, check where the noise is coming from and replace noisy fans with "quiet" fans - These are often temperature controlled so that all the time it's relatively cool inside your case, the fans will run at an idle speed thus greatly reducing noise. A noisy hard drive generally isn't a good sign, but it is possible to buy hard drive enclosures which will reduce noise to some extent.

It is also worth tightening up any screws in your case as excess vibration can cause these to rattle generating further noise.