Well by process of elimination since reduced range is present with new transmitter, limited range activation must be caused by the receiver wireless entry module.new fob was programmed by jeep dealer with new maxell cr 2016 batterys. old fob did the same also.
I performed a Google search on 2004 Grand Cherokee keyless entry and there were multiple posts about poor range for the remote transmitter to lock/unlock the vehicle doors. It seems that the keyless receiver is part of the drivers side door module. So if the receiver is mounted in driver's door, it is very likely that the receiver antenna has become entangled in the window lift mechanism and is damaged. This would cause poor range reception for any remote transmitter.