Welll from what I gather, a deliquency stays on reports for the min. of 7 years, has it been that long/longer? If not they may of took it off your report themself. As for the cap one card im not sure, lol not a helpful answer I know, but keep in mind cap one pulls all 3 of your reports regardless of the card applied for. Aside frim that someone else may be more help lol.
Do you have anything on your reports at all? what about negatives? if you don't have any negatives you would be much better off apping somewhere like Discover, BOA, or Chase where you can recon and explain your situation and get approved for a card that will grow with you.
Please share a little more about your credit profile and there are quite a few people here that will be able to help you.
try ge cards.Sorry to hear about the itheft.good luck