Text frame doesn't accept text

I have a number of small text frames with one character each in them in a specific area of the document. Maybe I inadvertently changed some settings by stroking a wrong key, but all of a sudden all those small text frames because overset, with the character no longer visible and the little boxed + showing instead. 

I deleted all those small text frames, but now any text frame that I draw in that specific area of my document does not accept text. When I draw a text frame, the outline disappears instantly and there is no cursor.  The text frame is there, but if I try to type any text, even a single character, the text frame becomes overset, and all I see is the little + in a box. Note that outside the specific area, text frames work OK.

Any help much appreciated!