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You can go here http://www.sos.state.al.us/sosinfo/inquiry.cfm?area=Corporations and check to see if it is still active or not. Some states will allow/require a filing for "reinstatement" which is usually faster, easier, and cheaper than setting up a new corp.
The business license and the corporate charter are separate items in Alabama. Your charter may, or may not, remain active whether you have a business license or not.
If your corporate charter has been forfeited administratively, for example because you did not file your "privilege tax" returns, you may apply for reinstatement.