Q: Can't access my serial #, forgot password

Hello, I want to access Apple support to work with me to get my Airport Time Capsule set back up and running correctly.  I accidentally did a hard reset this morning, as I wanted to reset my password (forgot my current password).  So, I can't figure out how to reset my password now... and to get access to my Time Capsule serial # (required for Apple Support) it "seems" I need to be able to get into my current set-up to find the serial #... which requires my current password (again, I don't remember it).  So can someone help guide me past this frustrating loop that I perceive I am in currently?

Apple online support keeps asking me for my serial # to move forward in that process, and I can't seem to access that without knowing my current password, which was my original problem to begin with..??

Thanks!