Two parts to this one. First, that "Compatibility Mode" thing means you're editing an old Word 97-2003 format document (*.doc) instead of Word 2007's native .docx format. That's not the problem.
The problem is that you have a trial copy of Microsoft Office that was good for 25 uses (of all Office programs combined) or 60 days. At the end of that time it stops letting you edit your files or create new ones. You have to purchase Microsoft Office 2007, or at least Word 2007, to do that.
Note: The 25-character product key on the computer case or laptop bottom is NOT the key for MS Office. It’s only for the Windows operating system.
Here are some of your options for paying less than full price for Microsoft Office 2007:
First, if you're a student, you may qualify for the Ultimate Steal edition of Office at a pretty good price ($59.95):
http://www.microsoft.com/student/discounts/theultimatesteal-us/default.aspx
Second, if you’re interested in buying just Word, check out this URL, especially the second group of listings.
http://office.microsoft.com/en-us/products/FX101754511033.aspx
Note that the higher of the two prices quoted is for a full version of that program and the lower, for upgrades from existing software. Read the list of upgrade-qualifying software carefully: MS Works is often one, and may have come on your machine.
Finally, if you have files that are locked up in the new Word 2007 file format (.docx), here’s a possibility for salvaging them. Microsoft offers a free Compatibility pack that allows earlier versions of Word (and Microsoft Works) to read and write Word 2007 files. If you have access to an earlier version, this can at least give you back your documents. Some new features of Word 2007 will be lost or converted to straight text in the conversion to the earlier version.
Good luck.