PCIe network card deactivate DVI output (but NOT VGA output) on Shuttle SG41J1+
Solution 1:
It's the Intel chipset that's doing it, and it'll never change as it's a hardware/chipset limitation.
When you install a PCIe 4x or better card into the x16 slot it turns off the DVI and leaves the analog VGA port enabled. If you install a non-video 1x PCIe card, both video ports will remain active.
If it's a video card then regardless of PCIe channel amount (1x, 4x, etc.) both on-board video ports will turn off.
I just went through all this fun on a DQ45CB (same on-board graphics as the G41-series) trying to get a 3rd monitor working. :)
Intel's DQ45CB specs document actually has a pretty good table:
Not the answer you were hoping for I'm sure, but it's the way she goes. ;)
Solution 2:
It sounds like you're on the right track, it's likely a resources issue. Check the motherboard downloads page for bios updates, if that fails to render any results, go into BIOS disable the fast/quick/quiet boot for the next fire up. Before exiting reset resources if able and with the card installed. If the BIOS can it should shuffle any resources being double claimed as some devices still do. Save the settings and reboot into windows.
You won't know if your successful until all drivers load but the only reason this would normally fail is that on micro boards manufacturers often sacrifice extra resources to keep the density of the board lower. The assumption for most manufacturers is that the only card you as a user would know about fitting the x16 is video and therefor many of them don't consider resource sharing with alternate devices like they do for larger boards with multiple PCIEx16 slots.