I don't ever turn off my monitor when I shut down my computer, as it puts itself to sleep until I turn my computer back on, then I get the "No Signal" on the screen of my monitor.
When I turn on the computer, the monitor turns on as soon as the O/S kicks in.
Go into the Device Manager and see if it is detecting your video card, if not you'll probably have to update the drivers.
would help if we knew your system specs including make/ model #, etc.
***Incoming wall-o-text***
I'll do my best to describe what is going on.
Over the last month my computer has been changing its resolution on its own. I'll leave the computer and then come back a couple hours later and it went from 1440x900 to 800x600 "Honey the desktop thingys are all big!".
Lately when I turn on my computer I can hear it boot up and run the opening Windows Vista sound buuuuut, the screen (HPw1907) is black. WHen I turn on the monitor it displays a "No image" message and then goes to sleep. When I disconect the cord from the monitor it says "check cable connection". Here is the kicker - I dragged my 42" plasma tv and plug it into the computer and it is perfectly fine.
While on my TV I checked the display and it seems like the graphics card (i believe it is a GeForce8900) I have is trying to send the display in an aspect ratio beyond what my monitor is capable of. Oh and the 1440x900 aspect ratio is not a selection for me to pick.
I've ran a couple system restores and that has worked in the past but it continues to go black. I dont want to have to lug my 42" tv around just to get my computer working.
Please HALP.

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic