As it is difficult to determine the exact issue without the exact message you received, and the timing at which it appeared, I have sought out and am providing you with a number of pieces of information. One of these should apply to your specific situation, based on your description, and lead you to the solution.
In regard to the general question of ID vs. key, most references to those two terms actually mean the same thing, but to be technical, the key is usually generated within the software during activation, and an ID is more likely to come from the CD or case. This most often depends on an individual's preference for how the terms are used. However, one quick way to tell (as I am not sure where the key you refer to came from) is that keys are 25 characters in length.
Some folks prefer to handle matters by phone ASAP without trying to solve issues on their own. If you prefer to attempt to get telephone assistance from MS (without charge), the number varies depending on the exact issue. Issues of this nature primarily involve the activation process. If the copy of Word has previously been activated (which you can verify, as if it has the Activation Wizard will not start when it is clicked), you would need assistance to obtain a new key from:
http://support.microsoft.com/kb/823570/en-us
If it has not been activated, you would most likely be successful:
http://support.microsoft.com/kb/326851/
One consistent finding here was also to make sure that your system date/time is accurate. If you prefer to try the troubleshooting steps outlined for this type of situation, reference deletion of possibly corrupted files / other troubleshooting of a more general nature:
http://support.microsoft.com/kb/903275/en-us
Additionally, product documentation indicates that you should see a phone number specific to activating your product on your machine when starting the Activation Wizard.
With the above information, we should have been able to resolve your problem. If not, please post back and I will happily continue to assist. Otherwise, thank you for rating FixYa!