Word 2011: No new paragraph / line break possible in text box?
Before you begin, make a copy of the document somewhere.  Don't try this on the original in case you run into additional problems. 

Can you select the text before and after this text box? EG if you drag to highlight in the paragraph before the text box and you continue to drag (even if you have to go to the bottom of the document) down the document does it highlight?

If so cut that part of the document and paste it into textpad, then save it as a plain text file (use TXT; do not use RTF, RTFD, or DOC/DOCX) and quit out of Textpad.

Save the document, open it back up and open the text file in Textpad. Paste all the text from the textpad document back where it came from and re-apply your formatting. 

Sometimes, the document itself is damaged.  This trick might help.  Open the document and turn on invisibles (the backwards P in the toolbar). Now click in the document and select all. Scroll down to the bottom of the document, and while you are holding the shift key click just to the left of the very last paragraph mark. So the entire document is selected except the last paragraph mark. Copy what you just selected, open a new Word document, and paste. See if you can edit that text box in the new document.

And if none of this works at least you have an unchanged version of the document to continue to hammer on.