W124 Diesel glow plug system is not hard to fix. Here are a couple of things
you need to do.
1. Make sure the battery is new enough and got full charge. Most places will
test your battery for free. Autozone got the best bang per buck for group 49
2. Check your glow plugs by simply unplugging the plug from the glow plug
relay and check the resistance from the plug to ground (chassis). It should
all be like 0.5 or something like that. Make sure you got good battery in
your multimeter to do this test.
3. If all your glow plug check out okay and the battery is new/good. then it
is possible your glow plug relay is bad and you need a new one.
4 One last possibility is your ignition switch is wearing out so if you high
mileage car is giving you a bit of problem starting or AC fan issue, then it
is time to change it along with a new tumbler. You don't need the entire
ignition lock... just the switch and tumbler (tumbler: get from dealer and
they will match what you have and one brand new key.).