Shift lever won't go to park and moves stiff even while pushing on metal lever on the side of the transmission

The linkage may be out of adjustment preventing the shifter from moving into reverse or park.
One way to test this is to disconnect the linkage and manually move the lever on the transmision making sure that it can be set into park. Also try moving the lever counting each click from park to low gear to make sure it is clicking into each gear. If this works then the linkage is probably out of adjustment.
On the link cable there is typically a bolt in an oval shaped metal near the transmission shift lever.
1)Detach the shift cable from the transmission shift lever
2)Put the transmision shift lever in the park position, and also the shifter in the cab
3)Loosen the adjustment bolt
4)Reattach the cable to the lever
5)Tighten the adjustment bolt in place
6)Confirm that you can shift through all of the gears
Hope this helps

Rock the car back and forth to remove parking pin from park .

1. Position the steering column transmission shift lever to PARK (P).
2. Apply the parking brake.
3. Raise the vehicle. Refer to Vehicle Lifting.

1. Position the transmission range select lever to PARK (P). Rotate the range select lever clockwise until it reaches the full mechanical stop position.

1. Slide the black retaining clip forward on the range select lever cable end. This will allow the white lock button to be pushed out.

1. Push the white lock button on the range select lever cable end out. This will free the metal core adjust body which is inside the cable end. Do not push the white lock button completely out.
2. Inspect the metal core adjust body on the cable end for dirt or debris that may restrict the travel. Remove any debris by washing the cable end, the metal core adjust body, and the white lock button with soap and water. If the travel of the metal core adjust body remains restricted after the cleaning, replace the cable assembly.
3. Lower the vehicle.
4. Ensure that the parking brake is applied.
5. Turn ON the ignition switch.

1. Move the transmission shift lever from PARK (P) to 1 and back to PARK (P) ten times.

1. Place the steering column transmission shift lever in the Park (P) position.
2. Turn the ignition switch to the OFF position.
3. Raise the vehicle. Refer to Vehicle Lifting.

1. Position the transmission range select lever to PARK (P). Rotate the range select lever clockwise until it reaches the mechanical stop position.

1. Push in the white lock button in order to secure the core adjuster body inside the range select lever cable end.

1. Slide the black retainer clip rearward over the cable end until it covers the white lock button. Lock the clip over the cable end.
2. Lower the vehicle.
3. Turn ON the ignition switch.
4. Ensure that all the transmission shift light positions (P. R. N. D, 3, 2, 1) engaged and illuminate. If you cannot perform this task, repeat the cable adjustment procedures.
5. Ensure that the engine starts in PARK (P) and in NEUTRAL (N) positions only. If the engine does not start in PARK (P) and in NEUTRAL (N), the Park/Neutral Position Switch may need adjustment.
6. Turn the ignition switch to LOCK.
7. Ensure that the ignition key can only be removed with the transmission shift lever in the PARK (P) position.
8. Start the engine and check the vehicle transmission shifting. The range select lever cable is properly adjusted if the steering column shift light positions are the same as the transmission engagements.

I'm going to say something happened to the cable between the shifter and the transmission. There is a switch on the transmission that prevents you from starting the engine in anything other than park or neutral. The transmission is probably in reverse or drive which would allow it to roll.
Someone would need to check the lever on the trans where the shift cable is attached.

Sounds like you need a new shift cable. Remove the shift cable from the linkage on the transmission. If the transmission linkage moves freely back into the park position and the shift lever inside the car still will not move back into park than the cable is bad. If the transmission shift linkage will not move back into park with the cable removed than the transmission will need to be pulled apart to service the shift rod.

I’m happy to assist further over the phone at https://www.6ya.com/expert/jeremy_d728a59f986299fa

Shift - interlock system problem .
Automatic Transmission Shift Lock Control System
The automatic transmission shift lock control system is a safety device that prevents an inadvertent shift out of PARK when the engine is running. The driver must press the brake pedal before moving the shift lever out of PARK position. The system consists of the following components:
• The automatic transmission shift lock control solenoid
• The automatic transmission park lock solenoid
• The automatic transmission shift lock control switch
• The transmission range switch
With the ignition in the ON position, battery voltage is supplied to the automatic transmission shift lock control switch. The circuit continues through the normally-closed switch to the automatic transmission shift lock control solenoid. The transmission range switch provides a path to ground for the automatic transmission shift lock control solenoid in the PARK position. With the automatic transmission shift lock control solenoid energized the shift lever is mechanically locked in the PARK position. When the driver presses the brake pedal, the contacts in the automatic transmission shift lock control switch open, de-energizing the automatic transmission shift lock control solenoid. This allows the shift lever to move from the PARK position. When the shift lever is out of the PARK position the controlled ground contacts in the transmission range switch open. This prevents the automatic transmission shift lock solenoid from energizing when the vehicle is out of the PARK position.

The shift linkage is out of adjustment.

The cable bolt may be loose up at the column, the column itself may be loose enough to allow it to shift position as well.

Make sure column is securely mounted, If not- tighten the 4 bolts that hold it to the dash support so it is. if it is, crawl under driver's side and on the transmission is a bracket where the cable assembly comes into it, and from there a rod that attaches on the lever on the side of the transmission. Make sure the bracket is not damaged or cracked first- if it is, replace it. There is a captive clip to release on the wide part of the piece that the bracket holds, it does not come out fully, but it will release the cable housing so you can slide it to adjust it. With the column shift in Park position, note where the rod is at the transmission. Also make note if the bracket is in line with transmission. If bracket is in line, pull the lever rearward one notch/detent that you will feel engage the lever- this moves the transmission lever to neutral, then with firm pressure push lever forward so you feel 2 distinct notches/detents forward, the lever is now in park. Push locking clip back into position once you confirm the cable outer housing is squarely seated into bracket opening and is soundly clipped into the square opening of the bracket.

If the lever will not move to that second detent or you did not feel it, you will need to check by putting the column shift to first gear position, release the connection to the lever on the transmission just to verify location of lever, and verify the lever is indeed in first gear- the lever on the transmission will move no further- then count detents forward from the rear stop. you should end up in park, and you may hear the parking pawl engage the output shaft of transmission. move lever back to the rear to the stop, reattach the connection to the cable, put column in park, release the clip again and verify the lever is as far forward as it is going to move. Push clip into lock position.

Start Explorer, with foot on brake pedal, release the emergency/parking brake and see if the vehicle moves, or if it is truly in park. It should be in park.

If you encounter some dificulty with getting the column shift lever itself moved over to park- apply brake pedal to release the park interlock mechanism.

Had the same problem. to shift gear manually with your hands. Look under the brake fluid (about a foot down) and there is a flat piece of metal. On the end of it on the bottom is a little rod with a round end. That is where the shift cable connects. pushing it toward the driver side of the car will put it in park. And if you count the number of clicks from park you can change gears. For example: 1 click from park is Reverse, 2 clicks is Neutral, 3 clicks is Drive. That is if it is all the way towards the driver side. Don't force it. when it stops clicking dont push it anymore. Hope this helps.

Two things happen. On collum shift cars and trucks the bolts work loose out of the shift lever to the cable under the dash where the shift cable connects to the steering collum. the cable connects to a lever that is connected the the shift tube ( part of the steering collum ) bolt heads are 30 torx. the other thing that happens is the cable comes off the trans mission lever and it just snaps on. The bushing waers out and the cable just comes off the pin on the lever coming out of the transmission. Front wheel drive cars it's on the top and rear wheel and trucks it's on the side ( happens less on these and then the cable can break it'self, and the shift cable has to be replaced sometimes if the bushing in the end fails at the transmission end.

When you say it is broken do you mean it won't move into certain gears?

In past couple days our '04 Echo shifting lever won't go into Park or 2 or Lo gear. And we couldn't take the key out of the ignition. My husband took to center console cover off and when he loosened the bolt under the lever we were able to get it into park and get the key out. But still cannot get into the lower gears. Will probably be taking it to a transmission shop before making major decision.

If your's is an automatic trans, and it is locked in park, there is a small opening on the right/front side of the shifter, pop the top and press the white button, it releases the lever.

Good Luck!