Do you remember what credit card you used? If you still have the same card, they might be able to resurrect a payment record for you even if you have long ago tossed your old statements.
I make it a practice to file away my final billing statement from every cruise I take. It shows dates, cabin number, and any extra charges. Faxing them a copy of one of them got me credit for a Celebrity cruise I took years ago, beyond their records.