It's impossible to "re-install" a baseband, but you could just restore your firmware over and over until it works. If you're sure your SIM tray/reader aren't faulty, then try toggling Airplane Mode off until the "Carrier" button disappears from the menu and then turn off Airplane Mode.
That may refresh something. I donno, sometimes it works for me!
EDIT: Are you sure your antenna is good too? It may not hurt to crack open the phone (depending on how technically savvy you are) and see if all the wires down by the bottom docking port are connected properly.