Upgrading the Gateway LX6810-01's Power Supply and Graphics card

Hello friends: I found this community via a google search, and saw that it had many helpful technologically inclined individuals who are quick to help their fellow man, so I decided to create a post. So, onto my problem:

I recently bought a Gateway LX6810-01 at Best Buy (I know, retail) because I needed a computer asap for my work needs. However, I am also a gamer. I found that the onboard card runs quite a bit of games (even Bioshock), but I'm looking for a long term solution (I want to buy Crysis).

My dillema stems out of the fact that the power supply is a measly 400w. Now, I'm very adept when it comes to software, but my mind just goes blank when I open the case. I was looking at this graphics card, and quickly ordered it (it just came to my house yesterday). Sadly, I plugged it in, and after it failing to initialize, I noticed it needed 450w of power (50 more than what I have now).

So, I called a few friends, and found out I should upgrade to an 800w power supply, and I should check to see how many "pins" I have, to know whether or not I should buy a "20, 22, or 24" pin power supply. I honestly have no idea what to look for: but all I know, is that first things first, I want to upgrade my power supply, because 400w is pretty meager.

So my main questions are: is there a way to find out, easily, if this bus is "24 pins?". If not, how would I go about counting - what do I look at? Also, will this machine handle my new graphics card just fine if I upgraded the power supply? There's nothing else I should be worried about?