If your account was terminated for activity, I'm sorry, but terminated accounts are deleted permanently. There's no way to reactivate or restore your account. Feel free to sign up for a new account. Remember that it's required to log into the forums at least once every 31 days to keep your hosting account active. If you'd like, you can purchase an inactivity timer with your new account so that you don't have to log in for a year and still have an active hosting account.
Just to be absolutely sure, what was your cPanel name of your previous account?