What model is it? There is a history of problems with one model of the Sony. Here's a link to it. http://forums.afterdawn.com/thread_view.cfm/630661
I've got an older Sony model (a DCR-PC110 bought in 2001 and I still love it). On that model there is an item in the menu where you can switch output to LCD (and also to DV-out) between ON and OFF. Maybe it is set to OFF on your camcorder?