I purchased a Dell Slim Studio 540 in June 2009 running Vista Home Premium with an ATI 4350 and BIOS version 1.0.2. I have a DVI connection from the 4350 to the Dell VGA monitor (using a DVI-to-VGA cable) and an HDMI connection to my Panasonic 46" HDTV.
The PC will boot with the HDMI unplugged. If I plug in the HDMI after Vista starts, the VGA display will mirror onto the Panasonic. But the PC will not boot if the HDMI is plugged during the boot cycle. The PC will also not boot if the VGA is unplugged and the HDMI is plugged in.
I read about a BIOS fix in version 1.1.3 for a different Dell model, but I don't know if the fix applies to the Studio 540 and ATI 4350. Neither Dell support nor AMD support had any ideas on how to solve this problem.