Sometimes when I start or reboot my computer the screen stays black and won't receive signal from the display adapter. Rebooting the machine once or twice makes it work again. 

The weird thing is that if I have my headphones plugged in I can hear the Ubuntu startup sound and the IP address responds to ping. So that means the system doesn't hang, it just doesn't display the image. There are no error 'beep' sounds and no leds are flashing on the mobo. So far I have tried the following:

* another monitor
* removing the GPU and using the on-board graphics
* unplugging all SATA devices
* clearing the CMOS
* setting the default GPU in UEFI manually (tried on-board and PCIe both)

Any suggestions what should I try next? I have the latest BIOS.

*UPDATE* 
I tried the following:

* disabling the graphics adapter switching ability
* unplugging and re-plugging the DVI cable on both ends when it goes black
* swapping out the DVI cable for another one
* swapping out the monitor while it is still black

I haven't overclocked anything and increasing the screen brightness won't do it because the screen goes in sleep mode.

More details:

* KHX1600C9D3K2/8GX Kingston HyperX memory 8 GB
* XFX Ati Radeon HD 6850 connected to a single monitor with DVI
* Intel Core i5 2500K, LGA1155, 3.3 GHz
* SeaSonic M12 SS-500HM 500W power supply
* Samsung HD103UJ 1 TB HDD
* M-Audio Delta Audiophile 2496
* Grub dual boot Ubuntu 13.10 (was 12.10 when I first posted) and Windows 7