A new computer would be worthwhile but you can probably throw an HD4670 in there and it will let you play games well with good settings at low resolutions(1280x1024 and below.) The card is many times more powerful than your IGP if that's what you are using now.
It all depends on what you want to be able to do with the computer. What applications do you use and what level of gaming do you want to be able to do? What size of monitor will you be using?
Do you have a video card in the PC now?
What size, make and model is the PSU (I did not see it listed on the specifications)?
That CPU is getting old - but still can handle general applications, and as suggested above, if you are only using integrated graphics then a light gaming card would increase peformance substantially. Although whether it can handle even a 4670 depends on the size of the PSU.
Would you consider building your own instead of buying? It is really not hard to do and would open another option - to upgrade the PSU (if necessary) and graphics card now and carry them into a new build. Of course the graphics card could be carried forward even if you buy rather than build.
The specs say the power requirement is 400w but I ran a power calculator on your system and, assuming it has not been modified and nothing else connected to it other than 2 USB devices, the power requirement with the 4670 is only 212w.
This would be a good choice for a specific card due to the rebate:
The 4670 was one of the special items (out of all PC components) that were listed on Tom's Holiday Buyer's Guide 2008. It lists the Sapphire Radeon card rather than the MSI one, but the inclusion is really for the 4670 card and not that of a specific manufacturer: