How old is the phone? ive had a quick search on a N95/6 forum that im a member of and it looks like you might have a worn ribbon cable, which is why theres no display.

Not 100% sure but from what i searched on the site it sounds like the same issue you have.

If you want to have a better look yourself, or even register to the site http://www.n95users.com/forum/ and make a post, their very knowledgeable