Fixing a not working Power Functions L motor
Since the basic architecture of the motors in a line (in this case PF M-L-XL) are the same, the tips you have found for the other models would most likely apply for your case as well.

Otherwise I'd recommend some basic troubleshooting steps:


Ensure you have a working battery box and cable by setting up your functioning motor. Once you have confirmed that it runs OK, you can be sure that if after swapping the motor for a broken one, the problem must be in that motor.
Check if you can turn the motor's axle manually by inserting a Technic axle and turning it by hand. It may be more comfortable if you add a gear or a wheel to get a better grip. If you can't turn it at all or only considerably harder than the working one, you should suspect some mechanical failure (e.g. broken gears inside).
If you have a multimeter, you could check if the electrical characteristics of the broken motors match those of the working one. A significantly lower resistance between the contacts is a sign of a short circuit, while a significantly higher one indicates a broken wire. With a bit of jerry-rigging you could also measure the current flowing through a motor that should be running from a battery box and comparing it to a normal motor's to see if there is too little or too much current.
You could also try opening up the motor and checking for broken or burned parts, foreign objects or debris, etc. Note, the above guide is for the M motor, but the same principles would apply for the L motor as well.


If none of the above helps, try contacting LEGO, as they would be able to provide replacement parts or further advice.