If you played on the US servers and you still know your login/password, then you should be fine -- though there can be fringe cases.
If that was so but you can't remember your password, then contact customer service and explain your situation to them.
It's true that if you were on Euro-DDO then you're out of luck, but that shut down 13 years ago, not 10.
It's very rare for a product key to be necessary nowadays, but it can happen -- if you're in a peculiar case, then you'd need to login to your SSG account page and see what's there :
https://myaccount.standingstonegames.com/index.php
Be aware though that a recent update to the DDO Store has made some old codes and keys non-functional, so that if you hit a brick wall, only customer service may be able to sort things out for you.