I've recently built a machine with the following components:
AMD Phenom II X4 840 3.2GHz processor
Asus M4A88TD-M EVO motherboard
PowerColor HD 6850 1GB graphics card
2 x G-Skill 4GB DDR3 1333MHz memory
Displays: Samsung SyncMaster BX2350 (main display), V7 L19WD (secondary display). The connection is DVI to HDMI for the Samsung, DVI to VGA for the V7
Whenever I first boot the machine each morning, black horizontal lines are visible across the BIOS splash screen and also across the display when I see the hardware/memory checks etc. After the Windows loading screen (it's Win 7 Professional 64 bit), no video signal is output at all and I have to hard reset.
However... second time around, after the hard reset, it always boots fine with no problems whatsoever. As it only affects a cold booted PC, might it be somehow linked to the CPU temperature? I'm completely stumped!
Oh I see that you may suffer from a cold boot. I suffer from it too but only when I do overclock pretty high or underclock pretty low.
Boards that suffer cold boot cannot be fixed. People just get around the bug since there is no fix. You could RMA your motherboard to Asus since manufacturers are aware of their boards cold boot problems. Some of them have fixed this issue by making a new version of their faulty motherboards.
So if you don't want to return the board to Asus, here's how I get around that bug:
When you turn on your computer, press the DELETE key on your keyboard. The computer will go to the BIOS but you don't need to see anything nor change anything. You just have to let it there a few minutes. In the BIOS, the computer cannot use the latest technologies to save power nor modify the fans speed, so it's gonna heat to it's nominal temperature in minutes.
Then after a few minutes of heating, you just have to press the reset button (or CTRL+ALT+DELETE). It'll reboot but this time it won't do the cold boot bug since it's hot already.
btw, my motherbard is a Gigabyte GA-965p-DS3 rev 3.3 known for cold boot bugs on overclocking. This is the only way to make do with it.