2002 Dodge Intrepid ES shift selector is stiff, difficult to move into position. Is this a linkage rebuild issue?

This sounds like a shift cable linkage problem to me. Check to make sure the shift linkage is responding properly to the shift selector by having someone shift it while you watch the linkage under the hood. Also make sure there is nothing blocking the selector from moving and the cable is free of kinks and other cables or things pressing on it. Of course do this with the engine off for safety. Also try manually turning the shift selector lever and make sure it is engaging, there should be a nice stiff slick. If the cable and selector are working properly then you might have a bigger transmission issue on your hands.

Could be the brake switch (at the brake pedal) or the release switch( in the console)

run the fault codes and look for a faulty TCM unit.

Do you feel some play between the linkage parts?
If it's too much play, then that's the problem

Test/Service/Replace

The circuit on newer cars with automatic transmissions has a neutral safety, or neutral start switch installed between the ignition switch and the starter. The ignition switch cannot operate the starter motor unless the transmission is in park or neutral.
Late model vehicles with manual transmissions have a starter/clutch interlock switch that requires the clutch to be depressed to the floor.
Neutral Safety Switch
Normal operations of a neutral safety switch provides a quick check for the adjustment of the gear selector linkage.

• To do this, move the selector slowly until it clicks into the PARK position.
• Turn the ignition key to the START position.
• If the starter operates, the PARK position is correct.
• After checking the PARK position, move the lever slowly toward the NEUTRAL position until the lever drops at the end of the NEUTRAL stop in the selector gate.
• If the starter also operates at this point, the gearshift linkage is properly adjusted.
• This quick test also tests the adjustment of the neutral safety switch.
• If the engine does not start in either or both of these positions, the neutral safety switch or the gear selector linkage needs adjustment or repair.

CAUTION
Since you must work under the vehicle to adjust most shift linkages make sure you properly raise and support the vehicle before working under it. Also, wear safety glasses or goggles while working under the vehicle.
A voltmeter can be used to check the switch for voltage when the ignition key is turned to the START position with the shift lever in PARK or NEUTRAL. If there is no voltage, the switch should be adjusted or replaced.

repair the selector system first then ask what to do

YEP SHIFT LINKAGE LOOSE OR WORN NEED ADJUSTMENT.ADJUST THE SHIFT LINKAGE BY POSITION THE SHIFT LEVER IN NEUTRAL .REMOVE THE REAR TUNNEL COVER IN FRONT OF THE REAR SEAT.PULL THE RUBBER DUST COVER FORWARD ON THE SHIFT ROD.LOOSEN THE CLAMP BOLT ON THE SHIFT ROD.MOVE THE TRANSMISSION SELECTOR SHAFT ALL THE ITS LEFT STOP,KEEPING IT IN NEUTRAL.WITH THE TRANSMISSION STILL IN NEUTRAL . MOVE THE GEARSHIFT ROD TO THE RIGHT TO ITS STOP.TIGHTEN THE CLAMP BOLT TO 18 FT LBS.TEST THE SHIFT LEVER PLAY SHOULD BE THE SAME IN ALL GEARS IN ALL DIRECTIONS.

Have the throttle linkage adjusted by a transmission shop. Filter and fluid changed.

It sounds like linkage to me as well - jack car block to prevent fall and block tire - do on flat ground and track cable under car. I think you should start under hood where linkage joins transmission. I seem to recall a plate there to hold at this end . not that it is a yoke type movement in transmission. this must be always lubricated. Did you ever have car jump out of gear? was it ever stiff to shift and has car been sitting?

need to adjust the shift linkage