ATI and Nvidia Hardware Promotion Issues

I am encountering difficulty when attempting to activate games I received as part of a hardware promotion - what should I do?

Related Error Messages:

• This offer has already been activated using a different Steam account.
• This Steam account already owns the product(s) contained in this offer. To access them, open the 'My Games' list.
• Sorry, this computer does not meet the system requirements for the offer.
• Sorry! We require DirectX 9 or above to verify the eligibility requirements for the offer.

This offer has already been activated using a different Steam account.

The offer which you are attempting to register has already been activated on your machine. Please see the Resetting a Lost Password topic for instructions to locate the account the promotion was registered to.

This Steam account already owns the product(s) contained in this offer.

The offer has already been registered to your account. If the games do not appear in your account immediately, please exit and restart Steam to confirm whether or not the registration was successfully completed.

If the games do not appear in the Library section once you have logged back in to your account, please submit a support request.

Sorry, this computer does not meet the system requirements for the offer.

The hardware promotion does not apply for your machine.

If you believe that you have received this message in error, please follow the instructions in the Checking DirectX Settings topic to generate a DXDIAG report.

Sorry! We require DirectX 9 or above to verify the eligibility requirements for the offer.

This error message indicates that the version of DirectX on your machine must be updated. Please see the Checking DirectX Settings topic for instructions to update DirectX to version 9.0c or better.