What is the make and model of your motherboard? Also does it only have the VGA and HDMI ports; or does it have VGA, HDMI and DVI?
Reason for asking is my board (Asus M4A78 Pro) has all three, and any two of them can be used at one time. Specs on the 780G/HD 3200 chipset,
AMD M780G Specifications Quote:
ATI SurroundView™ Technology
Provides support for four or more monitors when you combine an integrated graphics processor (AMD 780 chipset-based motherboard) with a discrete graphics processor (ATI Radeon™ HD 2400 Series2 or ATI Radeon™ HD 3000 Series). Each additional discrete graphics processor can provide support for two or more independent monitors. The integrated graphics processor and the discrete graphics processor work in parallel to drive multiple displays.
Unfortunately I can't tell you how well it owrks or doesn't as I have never even enabled the onboard.
P.S. Even if both monitors were working, using a splitter will give nothing more than the same thing on each with no way of changing it.