The bottom half of the touch screen don't work
What can I do to fix this problem
Tammy Adams, you can try with a reset and a restore first. If that does not work, disassemble your phone, check the cable for proper connection. If it is properly connected, no corrosion or debris on the logic board, replace the digitizer. Check this video to see if you are up to that task. Also remember that the Original 2G iPhone Glass repair will cost you more than the 3G iPhone Glass. The 2G uses an assembly of the glass, digitizer, and LCD screen. the assembly is available at places like this. Hope this helps, good luck.
It must be the digitizer went bad, sadly its kind of expensive around $70 for an OEM lcd and digitizer assembly as they come as one unit.
Theres a guide how to replace the display assembly on a original iPhone and lots of videos on youtube.