Sounds like the end of the firing pin is broken off.
Order a new one from Kel-Tec.
1-800-515-9983 (Ask for "Parts Dept."
Parts to order:
P-11 Firing pin (Part No. 170)
P-11 Firing pin spring (Part No. 172)
P-11 Firing pin screw (Part No. 174)
Wear safety glasses. Parts can fly out under strong spring pressure
First, field strip the pistol.
Using a 3/32" Allen wrench, remove the firing pin screw while holding a cloth or rag securely over the back of the slide. When free of the firing pin screw the firing pin and spring will fly out the back of the slide with surprising force.
Clean the firing pin channel with a series of Q-tips, using a firearms solvent, automotive brake cleaner or even just rubbing alcohol if that's all you've got handy. Don't let the cotton tip get stuck in the channel.
Thoroughly clean the firing pin screw hole in the slide with a series of Q-tips. Thoroughly clean the threads of the firing pin screw also.
Install the new firing pin and either the new or old spring (your choice, the new one may be longer until it takes a "set"
, and get ready to re-install the firing pin screw.
Place the firing pin spring in the firing pin channel of the slide.
Insert the new firing pin into the firing pin channel with the notch on the big end facing up.
Start the firing pin screw in it's hole and run it in until about half of it is still protruding above the slide.
Place blue Locktite or another medium strength
thread locking compound on the exposed thread of the screw.
Never perform the following with the rear of the slide pointing towards your face
Using a flat ended rod like a dowel press in on the end of the firing pin as far as you can* and while holding it in screw the firing pin screw down until it hits the flat on the firing pin and snug it down gently. The firing pin should now be locked in place and not able to move.
Slowly turn the firing pin screw counter-clockwise 1/4 turn. You should hear the firing pin snap back against the retaining screw. It should now move freely (against spring pressure, of course).
Another method of installing the firing pin is to place the firing pin spring and then the firing pin (notch facing up) in it's channel in the slide and then slip the slide back onto the frame.
When the back of the firing pin contacts the hammer the hammer will force the firing pin in.
Push the slide back until it is in it's normal position when in battery and hold it there by wrapping your weak hand around the slide and grip while using your strong hand to hold the Allen wrench used to tighten the screw.
* You might want to do this while holding the slide inside a zip-lock bag because if the rod slips you will be looking for the firing pin and spring who-knows-where.