The monitor does not respond to turning on the computer

The problem was the graphics card.

Um... have you tried to unplug and re — plug the monitor?
if again does not help, then throw the monitor settings( through monitor menu, or hold down on/off for ~30 — 60sec).

Graphics card — ATI? Connected via VGA? Try a different cable.

Um... I Have a similar problem about half a year already. When you turn on the system unit the indicator light on the power button Monica blinks, no picture. After several on-off image appears normally. After restarting the computer (more precisely, after exiting the BIOS), the situation usually repeats itself. Also Gigabyte (model I do not remember, 19" LCD). Laces DVI changed, other system units are not docked.

Oh, IBM — used a few times with this monitor... solved normally — off computer, take out-insert the video card and an hour or two to read a book :)