Ash here from the Shopify team.
I understand you're having difficulty remembering your old account details. I'm happy to help out with this! I see you mentioned wanting to start a new account. Are you trying to access the old account to retrieve some data, or are you considering firing the old account back up and using it as a starting point? Either way, as long as you remember the email address you used to sign up for the previous account, you can use this link here to track the account down!
I hope this helps, and let me know be replying here if you're still unable to find the old account using the above link. I'll be happy to look into some alternative solutions.