Not necessarily. My phone had no display and no tv out. Long story short: I replaced the entire screen and it is now working again.

Long story long:
I just dropped my N900 two weeks ago near the shower. The back cover and battery flew out. A few small drops of water ricoched across the room and landed inside the back of the phone. I left it unplugged for 24 hours (I would have done more, but the liquid seemed like an insignfigant amount).

When I turned it on, there was no video; but the phone powered on, the keyboard lit up and there were system sounds like it was normal. I plugged in the A/V cable and got nothing.

A week later, I purchased a badly used N900 and took both phones apart only to discover that it was my screen that was broken. Now I have my working phone horribly scratched screen. Video out also works again.

One of these days I will try to put the working parts of this screen into my old screen assembly. Although I am not in a huge hurry because I can barely see the scratches when the backlight is on.

The positive aspect of having a scratched screen is that I am more violent with my stylus when I use the phone than I used to be. The stylus works great when you use tons of force.