2002 Mitsubishi eclipse spyder cannot shift the selector level out of parking position to other position even though the brake pedal is de-pressed and key turn on.

Something wrong with the shift lock system maybe. Safety system that won't allow the gear selector to move from park unless the driver is pushing the brake pedal . Do your brake light's work ? Does your caddy have floor or column shift ?
Automatic Transmission Shift Lock Control Description and Operation (Floor Shift)
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 the PARK position. The system consists of the following components:
• The automatic transmission shift lock solenoid (serviced as the automatic transmission shift lock actuator), as well as the body control module (BCM) and the engine control module (ECM).The shift lock solenoid is located within the floor shift control assembly with vehicles equipped with floor shift.
• The BCM controls the voltage supply circuit of the shift lock control solenoid. The following conditions must be before the BCM will supply voltage to the shift lock control solenoid.
The BCM controls the voltage to the shift lock control solenoid through the shift lock control solenoid controlled voltage circuit. The following conditions must be met before the BCM will supply voltage to the shift lock solenoid:
• The ignition is in the ON position.
• The ECM sends an input via GMLAN serial data to the BCM indicating the transmission is in the PARK position.
• The BCM determines the brake pedal is applied according the brake pedal position.
Since the shift lock control solenoid is permanently grounded, the BCM supplies voltage to the automatic transmission shift lock control solenoid, mechanically unlocking the shift lever allowing the driver to move the shift lever out of the PARK position as the solenoid energizes. When the brake pedal is not applied, the BCM turns the control voltage output of the shift lock control solenoid OFF, de-energizing the shift lock control solenoid. The de-energized solenoid mechanically locks the shift lever in the PARK position.
During remote start operation, the BCM will de-energize the shift lock control circuit, locking the shift lever in the PARK position.

Does the engine start ? Is this a automatic transmission vehicle ? Do the brake lights work when you press on the brake pedal ? It probably has something to do with the Automatic Transmission Shift Lock
The brake transaxle shift interlock (BTSI) system consists of the body control module (BCM), powertrain control module (PCM), BTSI solenoid, stop lamp switch, and PRNDL selector switch. The BTSI system prevents the driver from moving the shift lever out of PARK unless the brake pedal is depressed while in RUN or CRANK.
The BCM controls the output to the BTSI solenoid by grounding the solenoid which energizes it, preventing shifting out of PARK. When the BCM receives input from the PCM over the Class II link that the transaxle is in PARK and the brake pedal is depressed, it will stop grounding the BTSI solenoid or de-energize it which will allow shifting. After the transaxle is moved out of the PARK position, the BCM shall monitor the status of the PRNDL serial data message sent by the PCM and shall continue to de-energize the solenoid until the transaxle has been returned to the PARK position.
In the event that the serial data messages are never received (approximately 5 seconds) by the BCM from the PCM, the BCM shall de-energize the solenoid to allow shifting. The transaxle can be shifted from PARK by placing the ignition switch in the ACC position. This eliminates power to the solenoid.

If you battery is dead it will not work make and model would help

Don't know make and model but try putting your key in the slot if you have a floor shifter and see if that releases it cable probably broke you will have to leave car in nutral and set parking brake or get a spare key to leave in the slot

Vehicles have a safety system that won't allow gear selector to be moved out of park unless brake pedal is pushed ! This what Buick calls there's
Automatic Transmission Shift Lock Control ! Depending on make of your vehicle it mite be called something else . But all vehicles have it.
The automatic transmission shift lock control system is a safety device that prevents an inadvertent shift out of PARK when the ignition is ON. The driver must press the brake pedal before moving the shift lever out of the PARK position. The system consists of the following components:
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The automatic transmission shift lock control solenoid

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The automatic transmission shift lock control switch

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The brake to shift relay

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The rear integration module (RIM)

With the ignition in the ON position, battery positive voltage is supplied to the brake to shift relay coil. When the RIM energizes the brake to shift relay, the brake to shift relay switch contacts close suppling battery voltage 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 permanently grounded solenoid is energized. This locks the shift linkage in the PARK position. When the driver presses the brake pedal, the contacts in the automatic transmission shift lock control switch open. This causes the automatic transmission shift lock control solenoid to release. This allows the shift lever to move from the PARK position.

Your vehicle has a safety system that won't let you take it out of park unless you have the brake pedal pressed ! Your brake switch could be shorted inside causing fuse to blow !
Shift Interlock System A brake/shifter interlock mechanism prevents shifting the transmission out of the PARK position unless the brake pedal (2455) is applied. The system consists of the following components:

• an actuator activated by the key interlock assembly and brake pedal pressed input.
• necessary wiring.

The system operates as follows:

• The actuator is energized when the ignition switch is turned to RUN, locking the transmission range selector lever in the PARK position. When the brake pedal is applied and the stoplight switch (13480) is activated, the shift lock actuator is deactivated.
• The transmission range selector lever can be moved out of the PARK position.

The ignition/shifter interlock cable (3F719) locks the transmission range selector lever in the PARK position when the ignition switch is in the LOCK position. It also requires the selector lever to be in the PARK position to turn the ignition switch to the LOCK position.

Most cars you have to push brake pedal to shift out of park etc. the switch at brake pedal is bad or out of adjustment. God-Bless! Its at top of pedal arm.

Check the brake light switch located on the brake pedal arm. Its above the pedal under the dash and has a connector with several wires attached to it. The switch is either bad, broken, or out of adjustment. If you have to step on the brake to shift out of park there is also a another switch located there as well.

You probably have a problem with the safety switch on the brake pedal. It Usually has a manual bypass or release button some where on your shift assembly. You may need to refer to your owners manual or ask your dealer to help you find it. I learned this from my wifes nissan , had same problem. This would at least let you Drive the car to a garage.

there is an electronic sensor connected to the Brake pedal that releases the shifter if it messes up your not going to be able to press that botton for nothing sad truth your going to have go to the Dealer for service