There is a company in California called DT&T that you can send your computer to and they will check it out and if your display is bad it will run about $450 plus shipping to get it fixed. Now depending on if it is the display , as you have not indicated it was damaged, it could be the logic board. If that is the problem it would run about $365 plus shipping to repair.
You may consider buying the external video adapter for your model and barrow someones desktop monitor and see if it works fine. That will give you an idea where the problem is and if you have the space you could save a few buck and just use it with an external monitor until you have the funds to replace it. Don't just replace the screen because it is acting up. Make sure where the issue is first.
Here is the info on that company
http://www.dttservice.com/iMacintel.html
good luck