actually this MIGHT* (go and google reviews for this card on toms or anywhere else if you want to check whether it'll run 1080p) work. I'm not a low-end user so I'm not entirely sure.
However if you are trying to play MKV videos, you may want to try Media player classic and fiddle with some of the settings? I remember playing MKV vids on my netbook, unfortunately I completely forgot how to do it, you'll need to google it
I would look into the HD 5550 or HD 5570. They are more than capable of video playback and are relatively power efficient and relatively quiet. The HD 5570 consumes 19w while playing games so playing video will probably be around 12w - 15w. The HD 5550 consumes less.
If you want to spend a little more money you can buy a passively HD 5550/70 which will be silent, but you need decent ventilation in your case.