Does any power supply work with any computer?I am going to buy this psu  http://www.newegg.com/Product/Product.aspx?Item=N82E16817371035&cm_re=500_power_supply-_-17-371-035-_-Product   for this computer  http://www.bestbuy.com/site/Dell+-+Inspiron+Desktop+/+Intel%26%23174%3B+Pentium%26%23174%3B+Processor+/+4GB+Memory+/+500GB+Hard+Drive/9846086.p?id=1218183110027&skuId=9846086

That should be enough power if you don't plan on upgrading that integrated graphics. But form factor also matters and you need enough connectors. Do ask someone that understands hardware and has access to innards of your PC before you drop the cash. it's difficult to tell you exactly what you need over the internet.
 
Good luck.

Try something like this, it will handle most anything you throw at it. 
 
 http://www.newegg.com/Product/Product.aspx?Item=N82E16817341017&cm_re=ocz_600w-_-17-341-017-_-Product
 
As for upgrading that current computer. Find out what motherboard you have, possibly throw a Quad Core in there(If supported by mobo) and a GPU, and you will have a killer rig, also upgrading to a high end dual core is also another option which would be great for gaming. 
 
If you do not want to upgrade your CPU the E5400 is a proven overclocker, if that is something you are comfortable with. Buy a decent aftermarket heatsink and that thing can hit over 3.5gHz with ease, after that all that is left is to buy a new GPU. However with that case overclocking may be limited, possibly getting a new case (antec 300, cm690 etc) would eliminate that issue.