If you have more devices you can play around. Set up a VGA monitor as primary and a DVI/HDMI monitor as secondary. Set device manager to open right when you log in (make shortcut to devmgmt.msc in start menu/startup) and check if the second monitor is visible, if it gets disabled, disappears etc.
You may as well open CCC and try to resurrect it. Click the detect button etc. I wonder if the monitors are not even seen by the card, or it just doesn't give them signal.
And another idea:
I remember people having similar issues when the R9/R7 series came out. Their solution was cross flashing their cards. I'll be honest, I have no idea what controls APUs. Motherboard BIOS? There's another BIOS in the APU? Whichever is the case, it would be a good idea to check if that firmware is upgradable and if there is an update for it.
CPU: AMD Phenom II X4 810 @ 3120MHz | RAM: Kingmax 2x2GB DDR2 800 @ 833MHz| MoBo: MSI K9A2 CF v1.0 (BIOS: 1.D)| GPU: Asus HD 6850 1024MB (DirectCu) @ 835/1135MHz | Display: L24FHD | PSU: PC Power & Cooling Silencer 750 Quad | OS: MS Windows 3.11 Pro x64