No problem with skin, have used it myself, but it is totally fanart orientated, which does stress out the gpu more than a skin which is not fanart based.
I'm using a 4200+x2 with 2gb of ram, the real difference is my gt220 against your ati3300, I know it is capable of HD playback, but running Mediaportal is like running a game as it uses directx, so add that to playing full HD is the issue.
as you have already said 720p works fine, so I would say it is the gpu letting you down on the 1080 material.
I know a lot of people on forum are recommending 5450 or better, for dedicated cards for MP use with full HD playback.
Another user reported the same problem with the StreamedMP skin on a system with a Radeon HD 3300. It does indeed look like its performance is insufficient for that skin. You have to use either the default skin or use Maya (without Fanart).