First thing to do is uninstall the video drivers and restart the computer. Then update to the newest available drivers. If that doesn't work there are a few things you can try.

Rivatuner, the program you mentioned is a gpu functionality tool, which allows you to change settings of the video card in windows. For instance you can change clock speed, fan speed, voltage, etc. If it is an issue with heat (which it may be) you should either speed up the fan, or alternately send it back to the company with the complaint that it is not functioning under the conditions they sent.

You may want to check the voltage stability of your computer. PCI-express runs off the 12v rail, so boot into bios and check the system diagnostics. If the voltage is + or - 5-10%, you could have a voltage problem. Alternately, you can search for software that will allow you to see the voltages in windows, and check whether they are going out of range under stressful conditions. If power is a problem, you're probably going to want to send it back and make note of this.

If I had to guess it is a driver issue. Changing out hardware, even if it is from the same manufacturer can cause issues, so try the driver change first and see what happens.

exercise the recovery device on the comp..

maybe that will help...
im no comp expert though....

Good point. Still he stated that he removed the old drivers. The voltage/cooling that you mention could be possible.

truthiness - what drivers are you talking about? Just the graphics card ones, or the whole kit-n-kaboodle.

ATM, I've just began prepping my system for a complete Vista reinstall. I'm just backing up all my files. Once I've backed up these install files, I'll try completly reinstalling the chipset and gfx drivers (and any others you reccommend). If that doesn't work, it's on to the Vista reboot.

Should I had changed any BIOS settings when upgrading the gfx card? Like changing any voltage levels? All the guide told me to do was uninstall my old gfx card crivers, place in the new card, install new drivers. But the whole guide was very brief, perhaps it missed something.

Oh, and truthiness, could you explain to me how to actually work RiverTuna.

STOP!

Here is something to consider...
Your old card only used ~16 Watts power.
The new card uses ~138 Watts power.

That's one hell of a difference. If this Riva Turner doesn't work then this could be a issue to look at...

Sources..
7300 GS (Close enough)http://www.xbitlabs.com/articles/video/display/power-noise_7.html

8800GThttp://www.xsreviews.co.uk/reviews/graphics-cards/vvikoo-8800gt-max-1gb/

Could be looking at a stronger power supply (A power supply should be suggested in your video card manual). 

Quartz - Well, that's part of the problem. The graphics card DIDN'T come with a manual. It just came with a brief installation guide whcich consisted of:

"Remove old drivers"
"Insert new card"
"Insert CD and install new drivers"

However, remember that this PSU was chosen for the 8800gt, and the 7300le was just a temp card chosen because the 8800gt was out of stock. The PSU should be able to handle to 8800GT, maybe I need to change some BIOS settings to change the watts supplied to the gfx card.

Any hints on what I should look for when I go into the BIOS?

Ok, if the power supply is up to scratch...

Trying to think...
Only thing that might need changing is the preferred video input in your bios. Shouldn't really need to change voltages as most new computers automatically do that these days without the fiddly switches you used to get on the board.

I would double check that the old drivers were removed correctly then power down, stuff in new card...power up, put in CD when windows asks for it and restart again.

Right, I'm going to go in for a complete driver reinstall (for the second time). Shall I download the latest from nVidias site, or use the ones the card came with?

I would use the driver on the cd that your card came with, it maybe an old driver but it should work fine. You can always update it at a later date.

Make sure drivers are completly removed and not just re-installed over the existing ones.