Lost mine (80GB MGS) to YLOD years ago, sent it to Sony for repair, and didn't record the s/n :\
I was pissed when they removed Other OS. We used it in grad school to study gpgpu programming.
At least Sony sent me a ps4 in exchange for that broken ps3, lol. Still don't know how that worked out since I was told I would be getting a recertified ps3 slim. I didn't complain ^^
Found my serial number! I had recorded it before submitting the repair to Sony. Also found my 2008 receipt from Sears.