Display Driver keeps disconnecting and recovering successfully...

The machine I am currently having this problem on is a very old machine, bought in around 2003. It was pre-installed with Windows XP, and handled games and tasks extremely well; and the machine was very expensive at the time.
I upgraded this machine around 2 or 3 years ago to Windows 7 Professional, and throughout those two or three years (not so much before, but a lot now) I have been getting a persistent problem with the Display Driver disconnecting and re-connecting. This is extremely annoying, and happens EVERY SINGLE TIME I under-go a task that stresses the PC ever so slightly. The specs are here:

AMD Athlon(tm) 64 Processor 3000+ 2.00 GHz,
2.00 GB DDR2 RAM (mother-board does not support DDR3 or any more than 2GB),,
32-bit Windows 7 Professional,
ATI Radeon HD 3450 512 mb
Service-pack 1 updated earlier today.

I have heard rumors and others say that this problem relates with Catalyst, and the current display driver that is installed. I went onto the AMD website to find the latest driver, installed it, and still no difference.
I uninstalled every single component of Cataslyst, still with no visible luck. It even freezes on YouTube videos, the problem is THAT BAD. I even tried reverting to Window's default driver for my device, still no luck.
Bearing in mind this is not my PC anymore, it is a friend's PC now as I recently gifted it to him, so he could have a better PC than his old one. True enough, it is better. But it's still pretty awful at the moment.

I am no newbie in the field of computing, so I do not need to be metaphorically soon-fed with basic information, thank you :)

- LifeStealer

I had a ASuS 5450 that would BSOD or just gakk & recover - but essentially had the same symptoms as your card. The GPU was toast. Took 3 weeks but I got another one that you'd better not push very hard...
That card has slower memory than the Sapphire editions.
I'd swap it out - but that's just me; even the uninstall garb is much better than it was from back in the day.... you may be pleasantly surprised with the H.P. to $cha-ching$ ratio.

:)

The graphics card I put in the machine is the best possible I can, and I am 100% sure switching it out to an older one will still persist with the same problem. Is there no sure-fire way to fix this problem, I think it is to do with software, not the hard-ware.

^^^ Excellent advise above, but I would remove all traces of the current video driver with drivesweeper before installing another version. In some cases using the latest version of the video driver is not the optimal solution so you may have to experiment with older versions.