Do the easy thing first, since you do not have evidence of mechanical damage. Do you know if any work was recently done on it?
Air in one of the injector lines will make it miss. And you need to find out what cylinder it is. So when running, crack one injector line at a time at the injector. Just crack it and see what happens. The missing cylinder will cause no change in sound. A good cylinder will also miss and the engine will sound worse. Also, cracking the lines bleeds air out, so on the missing one, see if you are getting any fuel and give it a chance to purge any air. See any bubbles compared to the rest? Then tighten the nut and see if that cylinder picks up or not.
Air problems can that cause missing can be as simple as a clogged fuel filter, a partially closed fuel supply valve, a vacuum leak in the fuel lines or a cracked dip tube in the tank. Lots of older diesels have poor air management in the fuel and can't tolerate any air without problems.
If it is not an air problem and you are getting fuel delivered to all cylinders, then look for compression problems. It's likely that if it's compression it will miss when idling, and maybe not when working. If it won't hit at all you will easily see other signs like extreme blowby, erratic exhaust sound or puffing smoke.
When it's running, but missing, look at the exhaust for smoke. If the injector tip is broken off or the injector is not atomizing, you should see black puffing smoke and it will miss at light loads. A a bad injector can act like a bad exhaust valve.
None of that? Pull the valve cover and roll the engine over to TDC, compression/power, on each cylinder, and check valve lash and the general condition of the valve train. If all that looks good, roll the engine through intake and exhaust on each cylinder to check for valve movements. This can locate a flat cam or bad pushrod.
Do all of this, or at least everything related to fuel delivery, BEFORE a compression test, unless you have a very convenient compression gauge set up for your engine. When the injectors are out inspect the tips. Do the all look the same? Do they look burned? You can even to a casual pop test and atomization test by reconnecting the lines and rolling the engine over, with the injectors out of the engine. Just try to do it without bending the injection lines. Do all of the "clouds" look the same and "pop"to start? Is one dribbling?
Finally, please don't use ether, or at least know how to use it correctly if you must use it. It is perfectly capable of damaging pistons and causing compression problems that get worse and worse. Ether would be better named "engine death".
All of this assumes you want to play with it yourself because you could just trailer it to the dealer.
