Can the NVIDIA GeForce 9300GE run 2 monitors

Does the card have two outputs?

As long as the card has two outputs then yes it can.

From what I can see there are two version, one with a single output and another with two outputs. OEMs typically use the single output to save costs but you will have to verify by looking at the card and determining if there are two outputs. Both outputs, if presents, can output signals at the same time and thus you should be able to do waht your trying to do. However, if you only have a single output there is no way of doign what your trying to do without upgrading your graphics card.