New Custom Desktop Issues- Need help

I am a long time lurker of the site and I just powered up my first custom built desktop and am already having issues I am desperate for help with.

Here the story: Bought this computer from a friend who was getting rid of it on the cheap. He built it custom and it has worked great for him.
I moved off to college, and bought the PC from him, but kept it at home for awhile.
I decided I wanted it at college, so I had my family package is snug in a piece of luggage and take it out with them to visit me at college.
When I got the computer, the cpu cooling fan had fallen out so I plugged it back in and locked it back onto the motherboard.

I waited for a week for a power cord to come in because my parents forgot the power cord so I got a 16AWG cord from monoprice.

Anyways, I just turned on the PC for the first time and all was looking well for about 30 minutes, till everything crapped out.
Now I know this isn't a display issue, but its an issue that has display symptoms.
Attached is a video of what the display looks like.

Basically the display works great on startup, but after about 30 seconds from login, the computer goes fuzzy and everything freezes up.
I looked inside the computer and pulled some components to clean them out. Ran the computer and still had issues.

One thing I noticed which may have to do with something, but I am too nooby to know, is that these little capacitor looking things on the graphics card look like they were blown up. I'll upload a picture to show you.
I don't know if that has any effect on anything, I'm just trying to list all the symptoms.
I'm using a geoforce 7300gt

specs:
Tower- ATX Tc3j-4050
Motherboard- Intel dp67ba
cpu- i5 2500k
graphics- geoforce 7300gt
RAM- 2X4GB= 8GB Corsair RAM
HDD- 1TB and 2 TB drives

Thank you so much for any help!

http://youtu.be/g4aRYLf_roU - FUZZY SCREEN

http://www.flickr.com/photos/60170022@N04/8121041484/in/photostream - graphics card

Thanks for the help, I ended up ordering a xfx r7770 graphics card since I got it on the cheap.
Well, turns out, I don't think my computer has the 6 pin cable required to power the graphics card.
When I turn the computer on without the graphics card I get a series of two long beeps, a pause, and then two long beeps.
When I turn the computer on with the graphics card, I get the same series of beeps. (That is, without having the 6 pin on the graphics card plugged into the power supply)
My guess is its time for a new power supply, but that is just instinct telling me that. What do you guys think? Again, I'm new at this.

Here are the specs
Power supply- 450watt
Tower- ATX Tc3j-4050
Motherboard- Intel dp67ba
cpu- i5 2500k
graphics- xfx 7770
RAM- 2X4GB= 8GB Corsair RAM

Edit: Stupid me. I didn't read the side of the box, says 500watt power supply mandatory. So do those beeps indicated a need for more power or what?

Update: Tried the old broken graphics card again to see if it would even start up. Sure enough, nothing. Flashed on for a second but immediately shut off. I'm hopeless