I am buying a computer that comes with ASUS Pundit P4-P5N9300, Socket-775 GeForce 9300, DDR2, VGA, SATAII, GBLAN, Cardreader. My questions is: does "NVIDIA GeForce 9300 / nForce 730i" support 1920x1080 resolution?
The feature you are looking for is called "dual link DVI" or "HDMI"
dual link DVI is an older digital connection that supports high resolutions, HDMI pretty much guarantees 1080P support (1920x1080).
As far as i know, pretty much everything made today, even the garbage budget cards, will run windows in 1080P just fine. However, games will generally run like crap at that resolution, if you are thinking of doing that.
In other words: Yes, the Geforce 9300 does support the resolution, as in it can run at it (after checking newegg quickly, it appears all the motherboards with the integrated Geforce 9300 graphics have HDMI).
No, this would not be good for 3d gaming.