OK, to take your points in Post #6 in order.
Its definitely not a trial product ! Normal trial periods are 30 - 90 days depending on the whim of the supplier. However, you have the click-to-run version of Office 2010. I cheerfully admit I know very little about Office 2010 - I have used 2007 occasionally and my own version is 2003 ( Heavens, it's only two years since I updated from Office 97 ! ) but this knowledge article from MS casts some light on your problem and suggests places to find solutions :
The fact that it has worked for you for over two years suggests that it is a valid licensed product, so you should have an activation key for it somewhere, take a long hard look around your files, it may be there somewhere. Failing that, a phone call to MS Support may well get you another one.
Libre Office certainly, and I think Open Office as well, has the native file format extension .ODT, but both will happily open virtually any word processing document you throw at them, and will save in a huge range of formats. Formats include : .TXT; .RTF; .DOC ( Office 97 - 2003 ); .DOCX (Office 2007 and later). The only weakness that I know of is that sometimes when opening an XML type file (Office 2007 and later) formatting in the document is not always preserved, but this aspect has I believe, been improved with recent editions.
It is highly unlikely from what you say that anyone has locked you out of your Office, but a quick look at the knowledge base article referenced above suggests that your version of Office is a bit of an odd beast, with some specific requirements for it to work. Take a good look at the article.