When you say it won't shift Maggie?Do you mean it sometimes doesn't shift out of park to reverse and drive etc?
From you asking about the gear shift cable I gather you do mean the gear shifter isn't exactly engaging the reverse or drive or lower gears and it occurs regardless if the engine is hot or cold.If you're also having starting issues then I'd be thinking that the gear shift cable could be loose or out of alignment etc bec the cable would affect the neutral safety switch and that would cause the starter relay not to engage when you turn the key to start.
Are you driving the 3.3 or 3.5 Maggie? Regardless what engine the transmissions are quite sensitive due to them working via gears and electronic module control , plus the fact they use pressure switches + solenoids internally along with an internal module , also Dodge transmission fluids used in those transmissions have added chemicals to assist the different gears and variety of different fluid pressures.
Any transmission fluid will wear down to age and mileage and especially heat so keep in my that if the engine has run hot or ever over heated that would greatly add extra wear to the transmission fluid and filter.
Are you getting any engine light coming on or codes? Bec even the gear shifter internal transmission functions work via assorted different pressures and pressure switches , as well as solenoids and an a internal and exterior transmission control module=TCM the solenoid pack inside the transmission with the module in it an go bad or the TCM under the hood by the battery can cause issues.Also the wiring or low transmission fluid levels can cause shifting issues, plus the fluid or filter could be worn down or dirty and that too will can cause shifting issues.
Hope that helps and best of luck.By the way here is a few hints since I own and have fixed many cars like yours sometimes if you've shifting issues you could have a loose plug in connector over by the passengers side under the hood by the front firewall, this plug as I recall has either 8 or 12 wires going to it and it connects to the harness of wires that run to the neutral safety switch and also all the different pressure switches that shift the gears from park to reverse or drive etc.Note one of those wires could be faulty too but I'd first try and see if changing the transmission fluid and filter solves or improves the issue, especially if it's not be changed in awhile or the engine has run hot or over heated in the past.
Sometimes on problems like that what I do bec of the age and design of that vehicle I'll simply disconnect the battery for a good 20 mins to be sure the comp system will refresh itself fully , then if the gear shifting seems normal that tell me more then likely a TCM or solenoid pack is acting up.Just note if you've any stereo or vehicle security or alarm systems you'll need the proper code numbers and producers before hand.