You may have to see if you can get past the gray screen...
•Mac OS X: Gray screen appears during startup
•MacBook: How to find the serial number
Also, if you registered the computer on purchase, or not,
the Apple site online likely has the product serial number
along with any other hardware items you bought.
Odd thing is, I've found a list of items going back 10 yrs
with the serial number and other info; but can't find
the page URL now that I'm looking for it. The content
appears only if you are logged into the Apple site; so
that means it uses your Apple ID to get that history.
I'll look more for a time, but it's 12:45AM now.
Good luck & happy computing!