olthumpa, one would expect the coil to last longer then 3 years, more like 30 years.
There's 12V coming from the switch through the coil, then to the glow plugs. The glow plugs are wired in series. So if one connection is bad the circuit stops there. Make sure each GP wire has a good connection.
You can use a trouble light at each GP. With the switch on, so the GP's are getting power (CCW on my old tractors) you should have power before the coil, after the coil, and at each GP. This will tell you your circuit is working.
Since your GP indicator is burnt you could jump it with a wire and still do the test. It would also heat the GP's if you needed to start it. You would need to be careful to not leave the 12V to the GP's too long because it could burn them out.
Is the indicator actually burn so you can see a gap? Can you check it with an ohm meter, if not in 2 pieces to confirm it's an open circuit?