I'm not familiar with the games you are playing on-line games I think, and yes it is a weak CPU but it shouldn't have a huge issue powering a 7770 certainly it wont be giving big FPS numbers but it should manage 30-40 FPS in most games.
This review has it powering a HD 5870 which is quite a bit more powerful than a 7770 http://www.legitreviews.com/article/1301/11/
Have you tried it with games that are not on-line ? Could it be your connection causing the issue ?
Mactronix