My easyTRX will not send out its position. I get position from everybody else, so it is reciving fine, but not transmitting. For the test I have connected a Raymarine C70 with one easyTRX and a C120 with another easyTRX.

The first thing to check is if you set the dimensions A, B, C, D in the easyTRX software. Some plotters need that to show the ship on screen.There could be some more reason:
The Raymarine C70 and C120 have an old software that is not able to decode Class B AIS (pleasure boats) messages. They only show Class A AIS (commercial vessels).Please do an update to version 4.29. This is the software which is able to display Class B AIS!
When you turn on the easyTRX and the green light is on (yellow, red and blue LED must be off!), then you have to wait up to 3-4 min until the easyTRX transmits!