You can contact the EA support at https://help.ea.com/.
Your activation limit will be reset so that you will be able to play the game(s). I know that because I have already contacted the EA support to reset my activations for NFS Undercover. Here is a quick tutorial on how to contact the EA support:
1. Go to https://help.ea.com/, click on "Games" in the upper left-hand corner, type in the name of the game and/or click on the game in the list.
Note: I can't find NFS Carbon and Underground in the list, just start with NFS Undercover for now.
2. Select "Codes" as the topic, scroll down and click on the orange button which says "Contact Us".
3. Select your platform and click on "Next". Under the text "Please tell us a little more about your issue" type "Reset activation limit" or something similar.
4. Click on "Next". Here you can see the method(s) to contact the EA support. I recommend to use the live chat if it is shown as a contact method. An EA Game Advisor will help you with your issue if you explain the problem to him/her. Alternatively you can call EA using the displayed phone number (assuming it is displayed as a method to contact EA in the first place).
Since there is no entry for NFS Carbon and Underground in the games list, you can ask the advisor to reset the activations for these games as well and, if that's not possible, ask them how to contact EA to get support for these games.
