My $0.02... I've got a 4350 that accelerates all my content (SD & HD) just fine. My HTPC has an e7200, 3 drives, DVD, 4GB RAM, the 4350, 2 tuner cards and it pulls only 85-90w from the wall under normal use. I can't recall exactly what full load wattage was, but it was maybe 120w or so. According to a review I saw (I think from xbit labs) the card itself only pulls about 8-9w at idle and only 15w at load. I got this card to replace a 7600GT and the before/after wattage numbers were pretty close to that. So as long as it's a quality 350w (seems like it is) you should be just fine.
@spike - something is knocking your audio out of sync, but I'm not sure it's your CPU (is that a dual-core?). Codecs are a really fuzzy thing, not all the video cards decode all the codecs so it would depend on what the MKV file was encoded with. Check out which ones give you trouble and see if there is a pattern. Use gspot codec appliance to see what codec is used by each file. See if some use drastically more CPU than others. If you're on windows, sometimes a codec pack helps... and sometimes it makes things DRASTICALLY worse, so a completely clean install with *only* the codecs you need might be the solution.