First.
Post a link to the data sheet. Not the sales advrrtisment.
Second. Get a separate 5v power supply.
Connect the separate power supply to the solenoid. See if it works.
Third. Calculate the base resistor value.
Fourth Add the TIP120 on that circuit. Add the proper wattage proper value resistor to the base and use a wire to feed it the signal.
Connect and disconnect the wire to test operation
If that works.
Connect your arduino ground to the other power supply ground.
Connect you output pin to the resistor.
Write a simple sketch.
post the sketch after reading how to post a sketch on the forum.
Important.
Make a sign.
NEVER CONNECT ANY COIL TO THE ARDUINO AS A POWER SOURCE.
if you are unsure of the defination of coil, please clarify its meaning.
To review.
Test coil by direct connection to a separate power supply
Test TIP120 by using wires.
Passing those tests
Prolerly connect the arduino low power logic to the base resistor, connect grounds, test operation.
POST TEST CODE
POST OPERATIONAL CODE
We want to make sure that you are not doing something foolish like trying to PWM a coil.