I have a 460W Cooler Master Psu and I'm wondering the same thing. A person on the internet answered my question and said he has the same psu and runs a 3870 just fine. Probably not very helpfu, but I would say upgrade ur psu as the answerer said the 460W would give out if the card was even more high end.
Are you using XP? if so then right-click on 'My Computer' and click properties, it should list the amount of ram you have as well as the processor and its frequency.
Then to find out the rest just look inside your case and count the amount of Haddrives, then look at the front of your case and count the drives you have, then list it here and I'll beable to give you an answer.