Stefan,
I guess you have to connect the one end of the trigger cable to the G68, and a polymeter on the other and switch the G68 on and check the readings on the polymeter -check the manual and if you get the G68/G55 specified volts/amps on the polimeter, then the G68 is ok and the G55 has a problem OR you need to see the trigger configuration on the G68.
From what I remember from the G68 specs it has configurable triggers, so maybe you need to set it up ...
That's all I can think of since I haven't had the chance to play with any of the above yet.
Costas