iPhone first generation LCD replacement
It's unlikely that the pixels have died, but the edge connector of the screen may have become dislodged or damaged, or it could be that the connection to the logic board could be loose.

You can try following this ifixit guide to see if taking it apart and reassembling it will restore any bad connections that dropping it may have caused.

If that doesn't work, you can just replace the display, as on pre iPhone 4 models the screen/digitiser and display are separate components, so if that's the only damaged component then it should fix the problem.