[mothered]

Was going to see if I could get away with just sending the receipt and saying I threw the paperwork/box with the serial number away upon opening the unit.

This Is on the grounds @"GosuSang" cannot provide you with the serial.

Try only sending the shipping Info and Invoice, excluding the serial number. They may accept It and If they don't, tell them you've made an honest mistake by forgetting to send It and need to locate It. They will not decline your claim for a simple memory lapse. Contact them again and advise that you're still searching for the serial and at the same time, be apologetic.

After all this, they could disregard the serial altogether. You have nothing to lose, and everything to gain.