It sounds like your high voltage is limping up to where it should be. (I'm assuming a standard CRT monitor - not one of those new-fangled flat things.) This is a fairly common symptom of advancing old age.
Quite often, replacement of a component or two can stretch the life of a monitor for a bit, but it's very difficult in my area to find anyone who will work on one at a price that will be less than just replacing an old one. There's the risk, too, that there's always something else ready to give up. It might be well to start collecting referals for "used computer" shops, so you'll have a place you can trust if/when you need to replace.
If the picture comes up to normal after a while, one option is to just not turn the monitor off when you shut down the computer (assuming it's not built into the computer). The turn-on "surge" is a stress on monitor components; so many people believe that monitors last longer if they're not turned off, and routinely leave the monitor power on. (You can tell your "green friends" that the power used by leaving the monitor on is much less than the resources consumed to make a new monitor.)