I second DC comments here.
Pull the carb off his machine and try it.
The stator and pick up coil can be checked with an ohm meter. It's in section 16-3 in the manual.
As for that other carb you pulled off of that trx250r, well that's one of those PJ series pieces of crap. I got some info off of another board and copy/paste it to word. I can't attach it as the extension is not allowed so I will paste it here. Hope you don't mind the long winded response.
PJ carb adjusting:
The following is not from Keihin or the internet. If any of it is incorrect I apologize and encourage corrections. It is also incomplete.
I thought it might help people to "properly" adjust the following section of these lovely PJ series carbs if they understood a little about how the idle speed adjustment/choke knob worked on them. Just skip down to the adjustment section if this doesn't interest you.
The PJ carb is obviously a weird bird. Imo, Keihin tried t do what is nearly impossible, which is to make a carb that would idle properly on all motorcycles it was properly sized for without having an adjustment for the slide. Obviously it didn’t work out completely according to plan.
Many people either give up trying to set the idle or simply live with either no idle or no choke, or use throttle cable tension to increase the slide height so their bike will idle.
The idle speed adjustment/choke pull knob combo, is nothing more than a fuel enrichment circuit.
The way this set up works in principal, is a bit similar to the Keihins on the ATC 250 ES Honda ATC. The main exceptions are, the PJ carb has an adjustable idle air screw and the Keihin on the Honda has a fixed size air jet. The air screw is able to adjust air to the idle circuit from an amount of 0 up to the size of the orifice it controls. The idle speed adjustment knob and choke pull knob on the PJ, performs the same function [works the same way] as the idle fuel screw on the Honda Keihin.
This combo knob has two sections. One section is a needle which is raised or lowered by turning the idle “speed adjustment” knob either in or out. The position [height] of this needle partially controls the amount of fuel supplied to the
Engine on the idle circuit. The idle circuit provides fuel to the Engine during starting also.
The other section is a plunger that when pulled, adds additional fuel to the bike for starting purposes only.
There are a few different ways to explain and approach the idle "speed"/choke adjustment of this lovely design, the following is just one. Some of these items were mentioned above by others.
IDLE "SPEED"/CHOKE ADJUSTMENT
1. Check float level, if it is too low it can cause a lean idle condition, if it is too high, it can cause a rich condition. Set it to the lower end of the recommended height then check idle again before making further adjustments.
2. Make sure there is a little free play in the throttle cable.
3. Turn the air screw all the way in until it just barely stops and count the amount of turns. The average might be 1, the max might be 3. If it is less than 1/2, and your idle screw knob is at the max limit, your pilot jet is too small. I would install 1 size larger.
4. Warm Engine to operating temp then turn the idle "speed" adjustment knob [located on the choke pull knob] until the highest idle is reached.
5. If your idle air screw is more than 1/2 turns out, turn it in until highest idle is achieved but do not adjust it to less than 1/2 turns from fully closed.
6. Turn the idle "speed" adjustment knob until the desired idle speed is reached.
7. If your idle air screw is still more than 1/2 turns out, turn it in until highest idle is achieved again, but do not adjust it to less than 1/2 turns from fully closed.
8. Turn the idle "speed" adjustment knob until the desired idle speed is reached again.
9. Turn bike off and pull choke lever to see if it properly engages. If it does, you are done with this part, if it does not, install a 1 size larger pilot jet. This should hopefully create a high idle and/or rich condition at idle, in which case, you simply turn the idle "speed"adjustment knob in until the desired idle is reached.
If you turn the idle "speed" adjustment knob all the way in and the idle is still too high, simply turn the idle air screw out until the desire idle speed is reached.
If you reach a point where the air screw suddenly has little to no effect on the idle speed, you have reached the maximum range of its effectiveness. Count how many turns out it is from full in and make a note for your records. This point might be around 3 turns out from full in.
If you reach this point and your idle is still too high then the easiest way I know to achieve your desired idle speed is to reinstall the previous pilot jet, raise the slide a hair by putting tension on it by adjusting the throttle cable [this is not recommended because it can possibly create a potentially dangerous situation], return your air screw to its original setting and turn your idle “speed” adjustment knob in until the desired idle speed is reached.
You will need to fiddle with balancing all these things until the idle “speed” adjustment knob is in far enough that it allows the choke to properly function.
Ok, now if you eventually become one of the lucky few that are able to achieve idle nirvana with a PJ carb, but you now have a slight rich burble/hesitation just off idle, lower your needle 1 position at a time by raising the clip on it and PRAY that it goes away and does not affect your idle.
FLOAT LEVEL - Kehin says it is 16 mm on all PJ carbs.