That makes it an early 2008 model. I'd say most likely failure is the GPU - depending on which version of the 2008 iMac, might be an ATI HD2400 or 2600, or an NVidia GeForce 8800. Those cards are socketed so they can be replaced without a full logic board replacement.
If you have a service center or Apple Retail Store nearby I'd take it in to be checked out. DIY replacement is possible but hard to confirm that's the problem so you might spend money on a card & not end up needing it.