The time from when the monitor receives power to the time it reports that it is not receiving a signal is preset in the monitor itself. How long it takes from the time your motherboard gets power to the time it activates the video card will vary with the temps in the tower. Therefor, it is possible some days to get the message from the monitor and not on others. In other words, I would not see this as relative to your problem.
Go into MSCONFIG.EXE and unselect everything in the StartUp, Config.sys, and Autoexec.bat tabs, click on APPLY and reboot the system. DON'T GO ONLINE AT THIS POINT! When you do this, you will be starting with no virus protection or anything.
If it seems more stable, then start reselecting things one at a time, with a reboot and trial between each, until it starts acting up again. The last thing you reactivated is the problem.
This is a slow process, but will eliminate problems with something running in the background causing problems. One little hint here . . . when you are reactivate things, if you don't know what it is for, don't reactivate it. Many (most) programs add their features into the startup routine without asking and you probably have a ton of stuff running that is not being used . . . but is hogging up resources.