When you go to: Tools > Options > Sync

Do you see your email address/user name on the top?

Oh, I forgot to mention that I’m trying to do all this on another PC, and I don’t have access to the original Firefox files. So I’m unable to locate the username somewhere at my side.

In your new PC, did you see an option like "Forgot my User Name"? in the "Manage Account" under the Sync Tab?

If not, I don't think it's possible to access your account unless you can get hold of your user name from your old PC.

Nothing like this :( I saw options to reset password\generate new key, but nothing about username.

I think you are out of luck, sorry.