what exactly happens when the computer locks up? does it just shut down, error out, blue screen of death? It's possible that a ram stick might be flaking out on you or your heat sink might be f'd up too. If you have a decent case try taking the removable side panel off and then give it hell and see if it still shuts down. Normally if the chip is running way too hot you'll start seeing drops in performance, like major chugging for any task, or the computer will suddenly shut down. Yet another possibility is that an IDE slot or cable is shot which would explain your computer freaking out when that device was being used intensively.
1. open the case if possible and run some processes that are making your machine shit out now. You can check to see if your heat sink is spooling or not here. Take a look at all the case fans in action also. No luck?
2. remove a ram stick (assuming you have multiple sticks) and see if that makes any differance. Try the other too. No differance put em back in.
3. trouble shoot each IDE device that would be in use with the processes that are causing trouble.
4. if you have the time do a complete reformat and hope it makes a differance. it could be as simple as sound/video card failure also. you can dissable those cards and enable your mobo sound/video chips. If all the devices seem to be working fine but your shit keeps crapping out on you it might be time to consider upgrading. It's possible that you might have a worn out tired mobo/processor that's ready to retire.
More details would be great but that's just what you should do to troubleshoot your system. Might also want to reload your BIOS if you've messed with those at all. More than likely this is a hardware issue though since software issues freak out pcs before they shut down USUALLY. Oh and yeah, be sure to get rid of all the dust in the case like dude said, that's super important!