To be accurate, the ATI card referenced by ScottC has 'Avivo HD' circuitry capable of offloading most of the decoding, found on ATI Radeon 3xx0 cards and newer; NVidia cards have a comparable Purevideo HD feature.
The hitch is finding software capable of using this circuitry. Some commercially available software is (PowerDVD comes to mind), but most freeware isn't.

I experimented last year with the aforementioned Radeon 3450 in a HTPC powered by a 2x1.9GHz Athlon, which on its own is slightly underpowered for 1080p material (some stuttering); with the Radeon and the Cyberlink codec from PowerDVD, playback was smooth. However, as pointed out by msb0b, it's all too easy to have to play a combination that will not be able to use Avivo HD, and in the end I just upgraded the CPU in that machine to a one capable of handling everything on its own (the 2x2.5GHz mentioned above is a safe baseline for an Athlon X2).

Given the trouble it is to get it working under Windows, I assume you'd be better off upgrading your machine (motherboard+CPU, and thus DDR2 RAM; a motherboard with decent onboard graphics e.g. AMD 690G or above paired with a cheap modern CPU will be enough and less power-hungry than with a dedicated video card), if you are not already familiar with such workarounds and setup under Linux.

BTW there is no use getting a higher-powered video card for movie playback, as the Avivo/Purevideo HD functions are identical throughout the lineup in same-generation ATI/NVidia cards. I find that offloading the decoding to the video card is not that beneficial from a power consumption standpoint, as while the CPU will consume less, the graphics card will consume more; this especially if the CPU can be fine-tuned with an utility such as RMClock, with higher usage thresholds specified before frequency increases (the default AMD and Intel drivers tend to kick the CPU up to full speed at the slightest provocation).