Hi Joerg,  you have the best equipment available installed. all parts are first class.

Of course you can check it with an SWR meter, but I am not sure if that will help you identifying the problem. Your antenna tuner (if it works fine) will make sure, that you the SWR is good, even if your antenna is not transmitting. In our typical boat installations the tranceiver will see a nice tuned antenna, even if it is just a piece of wire, because the antenna tuner simulates a nice tuned antenna to the tranceiver and the power might be used to heat up the tuner and not to escape through your antenna into the air - excellent SWR but nothing transmitted.
But the SWR meter would help you in finding out if your tuner is working fine.  Can you hear your tuner working?  It should "click-click-cklick..."  when you change to a  new frequency and transmit a low power signal for tuning. the relais inside make some noise when they try to "tune" the antenna to a new frequency that the tuner has not stored in his memory. 

I assume the setup of the tuner and the tranceiver has been checked.  You shall also set the AT140 in the IC-M802 initial setup as your tuner, you can also activate automatic tuning.

to summarize:

* check if your tuner settings are ok (I am sure they are) and that the tuner is tuning. If you have a SWR meter check that .
* make sure your existing ground is working by cleaning your dynaplate and make sure connections are good, no other grounding is necessary (see Oliviers post), do not connect your tank
* check if the GTO15 wire from the tuner to the antenna is free from any other stuff and that it is as short as possible
* check your antenna contact and make sure the antenna is away from other stuff that hinders transmitting (eg. I use an isolated backstay on starboard, but have to make sure that the the mizzen boom is on port when I transmit...)
* if nothing helps from the things above you should ask a local expert to check your installation (using a SWR meter, but also trying to find out what energy is really transmitted at your antenna, there are several options to do that)

what I would not recommend without help from an expert:
* changing your grounding
* opening the tranceiver and trying to fix something there

I am sure your problem can be solved relativ onsite easy by someone who is familiar with SSB installations on boats and who has the instruments to check it

best wishes, herbert SN120