If you have just bought it new then you need to send it back to were you bought it from. If not then it's rarely economical to fix monitors, the parts and labor usually end up more than buying new.
Presuming that you've made no changes in the power options panel and this is a sudden change without anything else being done to the computer, then this is a symptom of a dying monitor. I would guess that the capacitors that normally power the monitor up instantly are no longer doing their job, though something else might be the cause. In any case, unless its a very old monitor that uses tubes, the only cure is a new monitor.
However, to be sure of the diagnosis, you might try hooking your monitor up to a different computer and see what happens. If you don't have a separate computer, perhaps one that belongs to a friend. If the monitor starts up normally when connected to a different computer, that you have a problem in your computer. But if your monitor keeps up its ways, then its time to save up for a new one.