Diagnosis
The cold shot button mechanism is jammed. A small internal spring or the plastic plunger has failed, preventing the button from returning.
How to Fix It
Unplug the dryer. Carefully pry off the cold shot button cap with a plastic spudger. Inspect the small metal spring underneath. If it's deformed, replace it. If the plastic plunger is cracked, you need a new button assembly. Reassemble ensuring the button moves freely.
If That Didn't Work
The microswitch the button actuates on the PCB is likely damaged from being held down. You will need to desolder and replace that specific microswitch. It's a standard 2-pin push-button switch.
Heads Up
Forcing a stuck button can break the solder joints on the PCB. Always open the case to diagnose, do not just press harder.