I had this problem on a c220cdi (2002).
The glow plug light went off about 10 seconds after the ignition came on, but as soon as I started the engine, the light came back on, and stayed on.
It turned out to be a failed glow plug. I opened the relay and put a multimeter between each connector (to each glowplug) and earth. They should read about 6 ohms, one of mine was open circuit.
I changed that glowplug and all has been well ever since.
Good luck.