Unless you know someone who has a disc you can borrow, I know of no way.
Download the v7 trial version (but act quickly as most sites are replacing v7 trial with v8 trial). Here is a v7 link. I believe the trial version has the complete program, but only a few basic templates. After installation you can use Help -> Enter Serial Number to enter your number.
Insanity is hereditary, you get it from your children
And if the OP does download the v7 trial... he should write it to a CD and put that CD in a safe place
Just to give feedback from another's users perspective: I downloaded a PrEl 7 tryout only to check if there is something wrong with my DVD-version (Photoshop Elements, PrEl double pack german). I had many troubles with that installation (but I still got a DVD).
So I tried to use my serial number on the back of the DVD case for the tryout startup dialogue but it says that it is incorrect. I can't find "Help>Enter serial number" (I mean a similar entry in german) either. But this should be no use if startup dialogue doesn't work either.
One of the great features of Adobe's product registration feature, is that when one registers their products, Adobe has their S/N in the database. The user can then obtain that, via their Adobe Account ID, or via a telephone call. This also helps Adobe retrieve the S/N most easily.
This database has saved many hours of anguish.