So In this I'll cover diagnosis, repair and also dismantling and assembly (most lighters designs' are a common principle... )
Ok so i got a slightly better camera than my phone, it's an ancient canon powershot A60, only 2MP but check out the macro in the pics, it was top of the range once upon a time and it shows.
Step 1: So what you'll need for this
- a small philips head screwdriver (the tiny ones) it almost alway philips head.
-a penknife or a small flathead screwdriver (for adjustments)
-a pair of pliers, needle nose are great her but I can do it with my fake leatherman start to finish (make damn sure the pliers aren't magnetized it's annoying)
-a safety pin or some thin tough wire or a drawing pin (you'll see what I mean if it comes up)
-some sturdy wire about 24awg (anything that fits will do (again you'll understand pretty quick) is handy
-lighter gas, really helps diagnosis, in fact try the first...
-You may need rubber tubing or a piezo spark depending how you broke it (if you dropped I already know whats wrong. the lighter in this is my drinking lighter because it's made of metal and I know how to fix it)
Step 2: Ok diagnosis time doctor
Fill it with gas and listen, it may leak for a up to 30 seconds but that's ok as long as it stops.
Push down the button, is there gas coming out and is there a definite click from the spark (if yes to both this will be easy)
If there's no gas coming out at the nozzle but it's going somewhere then the connection has been broken probably nothing more than the flexible gas line has slipped off the seat of the reservoir end (there's more room here so it fall off that end but it's easy to fix anyway)
If you push the button all the way down and no click go to the shop and buy a really crappy cheap electric lighter, not a bic though, their piezios have no wire.
try turning down the gas a bit (sometimes the gas can't ignite because it going too fast for the tiny arc to heat... This always happens if you set the lighter when it's hot because it starts easier but wont once it's cooled down again.
All of these things are curable, this lighter hasn't many original parts, at one point I was going to hotrod a second nozzle in but There's no room, eventually I'll make an instructable about how to make your own jet lighter.
Step 3: Opening your lighter up
First look on the bottom, there should be a small (mostly likely philips head) screw not far from the filler valve, unscrew it, usually that is the only thing holding a lighter together, now pull the casing down off the rest (hold on to the cap and carefully pull the casing off) now you should see the guts of your lighter, there's probably 2 pins holding the assembly together. Enter the safety pin, Use the pin or wire to push the pin out of its hole.
now try moving everything apart, careful not to lose anything (yes my pins are made from steel wire but shh the screw came off a tiny circuit board, i didn't lose it, the screw was too long to start with.)
Check the image, the parts should be recognizable, and the note will explain all...
Step 4: Adjusting the spark
Basically the piezo is grounding out to the body or the chassis...
All we need to do is move the wire out and put it against the nozzle so it's touching it, that'll be guaranteeing near 100% performance in lighting. The first picture here shows the spark wire end pulled out and away a bit to so we get a clear idea of where we can put it. Wrapping it around the nozzle is good if there are no close metal body parts but the best is definitely doing it like picture 2. You should have kept all the pins, but really you should hav just left it together had this been the case. Before putting the case on, see if the lighter fires up if so slide the case on again and see if it still goes, if yes screw it back on and go light something up with it (In my case a Marlboro Red but in yours it may be a fuse... )
Step 5: So I did that, but I'm not getting anywhere
If the gas still isn't getting out the nozzle then the nozzle's clogged, symptoms include the lighter bursting into flame for a second during use. take some thin wire or a pin and put it through the nozzle to clear it.
At this point I can't think of much else to go wrong, if the gas filler valve leaks when you fill it up then tighten it. If everything works but the lighter won't light or can't hold a flame turn down the gas flow a bit. If the flame sputters and has trouble keeping going then it's too weak to stay above the nozzle, turn the gas flow up a little. Finally we put it back together.
If there's any problem I have missed comment me and I'll add steps, to be honest I can't think of anything other than components going wrong after this.
Step 6: Putting it back together
From the picture you should be able to tell your own parts easily enough.
This list goes bottom to top in stacking up the components again, refer to the pictures to make full sense
-gas valve lever (best put in before piezo for convenience
-lid top assembly (make sure the gas tubes go back in the right place)
-slide the cover back on and screw on