If the goal is to use extend mode to display different information on both screens, then a HDMI splitter will not work. Doing so will result in the same information being displayed on both screens because the HDMI port will only send 1 video stream. It is not meant to send two different video streams.
If the onboard ATI HD 4200 has a DVI-D or VGA port, then that should be used to set up an extended display since a seperate video signal can be sent out of those ports.
Your last resort is to purchase a video card which can cost up to roughly $50 for your purposes. Nothing fancy a HD 4650 should suffice and both monitors should be connected to the video card.