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If you don't know your Google account password.....you can CREATE a new Google account and use the NEW account instead of the OLD account.
Your HTC Phone only requires a Google account because it uses Googles Operating System. Called Chrome....or also called Droid.
In any case.....it would be best to use your old account.....but if that's not possible.....we can just create a NEW account, and use that instead.
But on your phone, you have to go back to ENTER A NEW ACCOUNT.