Hi Heather, do you still have your old computer or previous installation? If so, you could pull the serial off of your existing system by following the directions given here.
Otherwise, you may find your serial number in your online Adobe ID account, if you purchased direct from Adobe (or ever registered the software).
Hope that helps!
Try logging into your account at Adobe.com.
When I do that it gives me a page that includes "Plans and Products". I select "View All" and on the next page I select "View Your Products".
That gives me a list of every product I have ever purchased from Adobe along with the serial number.
Give it a try.