So with the HD 5450 machines, the monitors are connected by using the VGA and HDMI outputs, correct? And this works fine and extending the desktop isn't a problem, correct?
But with the HD 2400 XT, the monitors are connected to a splitter in the DVI output, correct? And this configuration doesn't allow for desktop extension, correct? And the main focus is on getting this PC configuration to support two monitors? If I'm not mistaken then this will go back to my earlier post about the splitter only allowing duplicate. Think about it this way: the graphics card is only outputting one source through the DVI port at any one time. (Still intrigued as what you wrote earlier implies extension previously worked.)
While doing a bit of research, whether the PC can use onboard/integrated graphics as a second display output will depend on the motherboard itself. It will require going into BIOS and checking what options for video display are available and the motherboard's display output.
The only thing I can think of as a possible get around for the HD 2400 XT with the splitter is creating a custom resolution, and fiddling with the monitors' positioning of the desktop to replicate the illusion of having an extended desktop. (Not sure if that even makes any sense....)