Did you register the program? If you did, the serial number will be listed in your account at Adobe.com. If not, I'd suggest calling customer service and see if they have a way to issue a new number if you can provide proof of purchase.
You might also want to go through your trash...
I went through the same thing with FrameMaker. You just have to figure out
how to navigate the difficult Adobe site-web to get to the place where you
can write an email to the correct department, and you must also
scanthem the receipt and anything else you have, and if it's the latest
version of InDesign you're talking about (and you have the receipt) you'll
get a replacement s/n. If you have an earlier version, you may have to
pay for the update. If you have no proof, and also if your version is very
old, you'll get nothing back.
Best thing, if you can't figure out what to do, is to get on the 'live
chat' (again, good luck with the site-web) and explain your problem, and
you'll get directions.