You should check for the leaking caps now. If you tell the supervisor you actually saw the leaking capacitors, she will give you a lecture about not opening the iMac, but this will help to ensure your repair. Once Apple runs out of motherboards worldwide, that's it - there will be no more free repairs. The good thing is that they will ship motherboards in from other stores to facilitate your repair. I had two eMacs repaired - they had the 1.25 GHz board in stock, but had to ship the 1.42 GHz board in from another state.
Serial numbers don't matter, either. All that matters is that there's visibly leaking capacitors.