You really don't need a quad core although since you bought it, then guess not important.
I have a couple of older machines, 2.2ghz dual core AMD Socker 939, and with ATI 4350 still hardly use the CPU during HD playback as the ATI does hardware acceleration. I know 1080p H264 are more demanding, but even so bet play them without any dropped frames.
Not to up on that IGP, but it should have HD acceleration built in. If you don't want to use system RAM (had problem with mine with Nvidia 6150 seemed to cause vsync like tearing) just get a cheap card, ideally passive, low heat and power £50 or less. For £25 or so, it's worth it as you're freeing up system RAM (how much have you allocated in BIOS?) Although I guess your IGP is probably superior to 4350.