keep the sink, toss the fan if it's stiff or stuck. you'll want to remove,clean, and regrease the sink as the old stuff will be crap. if you replace the fan, get a ball bearing fan. its a little noisier but will last 10x longer than a sleeve bearing fan.
leave the system the way it is. you will gain nothing by changing or upgrading the memory. unless it's defective... let it be
pull apart the power supply and check the capacitors in there. they might be starting to blow up on you. if you're up to it, replace them...otherwise, replace the whole power supply.
check the caps on the mainboard too.