If you take it to an Apple Store, ask if a Depot Repair is available for your model. That means instead of fixing your computer in the store, they send it to a central Apple refurbishment center where they fix just about anything they find wrong (other than accidental damage or abuse) for a flat fee. If the display is bad, the flat fee goes up. Other than that, the base fee usually covers everything.
I don't know what the fee is for an IMac, but at one point when a MacBook pro logic board replacement was $800-1000 in-store, the Depot service flat fee was about $315 and some people found out the center had replaced other components in danger of failing, like optical drives or wireless cards.
This service may not be available any more, or maybe it was only for easily-shipped notebook models, but it is well worth the asking if yo uno longer have warranty coverage.
The only downside to the Depot Repair is that it takes longer than the in-store option. However, when people were having their MacBook Pros serviced this way, they were reporting 5-7 days door-to-door.