[Donna Smoot] “My issue is that on the new computer is a Word for .mac Trial program. Whenever I click on one of the .docs from my desktop to have it open, it automatically triggers the Trial program asking me if I wish to use it”
All you have to do is simply trash the trial version (and empty the trash) and install the full version. then remove the links in your dock because they are connected to the trial program, and add links from the full version.
Also your subject heading is vary misleading. .Mac (dot mac) is a service that Apple sells (it is great by the way) and is has absolutely nothing to do with Microsoft office.