First, I think you need to contact the ebay seller and ask for that code. It is a very long time since I had AA 1.5 installed on a computer so honestly cannot remember whether a verification code actually came with the order confirmation for the disc, so was not printed on the disc sleeve.
I don't think version 1.5 required on-line registration and activation but if it did/does I fear you will be out-of-luck! If you read this thread, amongst many others, you will see that Adobe took the registration servers off-line several years ago. This particularly impacted registered users of AA2 and 3, but they are able to download a special installer and serial number which allows them to run AA3 without separate registration.
I don't think that applies to AA 1.5, however!