First hook it up to an external monitor to confirm that it is the GPU. These can often be reflowed with a hot air work station. I have had about a 70% success rate doing this. There are also repair services offered on eBay. Compare prices on a repair vs replacement and be sure they have a good warranty. Here's how to replace the video card: iMac Intel 21,5" EMC 2389 GPU Karte austauschen
@rany may also be doing this service now and shipping would be cheap on just the card.
@refectio may also be doing it.
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