It's often worth opening up the case when presented with a sick PC, before you plug it in. You may find bad capacitors, failed fans, dust-packed heat sinks, loose metal objects or case burrs shorting out circuitry, or damp / salty dust between the solder pads of chips, especially in the processor fan's downdraft area.
Fans and heat sinks
Generic OEM fans fail often, often starting with a harsh droning noise, then failure to spin up when power is first applied, before finally burning out and/or seizing up. I've yet to see a "boxed" Intel fan fail, but what does happen to older Intel systems is that dust can completely pack the heat sink fins, as in this partially-cleaned exhibit...

...where you can see the uncleaned fins to the right are completely packed and would pass no airflow at all.
Junk inside
When surgeons operate in body cavities, the operating theatre staff meticulously count swabs and instruments so none are left inside. Do the same with case screws, and don't put anything inside a case that you wouldn't expect to last for the next hundred years (it's hot in there; things die quickly).
This picture tells the hole story:

User tightens parallel printer plug screws, and when the plug is removed, so is one of the bolts that secure the socket in the case. When the cable's replaced, the nut inside the case is pushed loose; fortunately, the PC speaker's mounted at the bottom of the case and this eventually attracts and retains the loose nut. Good build practice would be to trap these nuts in place, using a mild stretchy contact adhesive, as on the left.
So, look out for this...

...and do this:

Metal objects inside the case are dangerous, whereas rubber bands are just yukky!


So don't rely on these to hold cables in place (or use paper-covered wire ties either); rather just wind cables loosely together so they keep themselves where you want them.
Safety first
Finally, look after yourself as well as your hardware, and don't lead others into temptation - for example...

...let that particular drive mounting screw go unused :-)
(C) Chris Quirke, all rights reserved; March 2005