You want to play a game on the same PC or do you want to capture console footage or something with a capture card?
In both cases you are pretty limited by your hardware, but for the second answer you might be able to get some kind of stream running. If you want to play anything but solitaire and stream at the same time I would definitely recommend an upgrade of your hardware. Get an i5/i7 system with a GTX 750 or something.
If you want to capture console input (or another PC) you might be able to get a stream around 720p running. But you will have to test a lot. For more specific settings we would need some more info about what you want to do :)