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Unscrew the mouthpiece from the pen again. Continue removing pieces until you are able to see the wire coil inside the heating chamber. It will be right above the lowest section, which contains the battery. Make sure the pen feels cool before touching it. The pen most likely won't heat at all if the coil needs adjustment. Don't touch the coil if you feel heat coming off of it. The coil screws into the heating chamber in 2 places. The first screw is at the bottom end of the coil, holding it in place above the battery. The other screw is at the top end, fastening the coil to the wall of the heating chamber. If the screws aren't in place, your coil likely isn't either. Take it to a vape pen shop to find replacement screws. The screws can come loose, especially after adjusting the coil. Unscrew the heating chamber if possible to access them. Use a small screwdriver or a toothpick to reach in and twist them slightly. Turn the screws clockwise to tighten them. Avoid tightening the screws too much or else the coil won't heat. Work in quarter-turns and test the coil as you go by turning on the power. Heating coil placement is a common cause of shorts. A paperclip is a good tool for reaching into tight spaces in the chamber and nudging the wire into position. Straighten out the clip, bending the end slightly into a hook. The wire should rest in space inside the chamber. Push the paperclip inside the chamber and use the hook end to jostle the coil. Only the ends, held in place by the screws, should touch the walls. Turn the power off before touching the coil with the paperclip. Metal on metal can permanently break your pen. Remove the paperclip and turn the pen on. If it still doesn't work, use the paperclip again. Lift the coil a little, then push it down gently to center it over the bottom screw. Nudge it to the side to align it with the top screw and walls. Then test the pen again. Once the coil begins heating like usual, put the pen back together. Unfortunately, aligning the coil isn't an exact science. Coils are finicky and it takes a little luck sometimes to find the proper positioning. The wire moves out of place easily as well. Dropping the pen, or even bumping it too hard, can cause it to shift. Your first option is taking the pen to a professional vape shop. Sometimes an experienced professional can find a way to repair it. If not, either get a replacement pen or purchase a new heating coil. Having a professional repair an old pen is often cheaper than replacing parts, and getting a new heating element can spare you from the cost of buying a whole new pen. Note your pen's brand to get an exact replacement. Usually the replacement is a whole new heating element, so all you have to do is unscrew the old one and affix the new one by hand.

Summary:
Take apart the pen to look inside the heating chamber. Check that the screws are in place. Adjust the screws to restore the power circuit. Straighten a paperclip to use as an adjusting tool. Move the wire away from the walls. Continue adjusting and testing the pen. Replace the heating element if the pen still doesn't work.