Tvheadend

You are missing libdbus-1-3, the tip is in the output of the "sudo apt-get install":

"tvheadend : Depends: libdbus-1-3 (>= 1.9.14) but 1.6.18-0ubuntu4.4 is to be installed"

From terminal or similar (its like command prompt in windows)
To correct give this a try:

sudo apt-get update
sudo apt-get upgrade
sudo apt-get install libdbus-1-3 tvheadend

If that doesn't correct it:
sudo apt-get install -f

Hope this helps

Thank you for the help.
Unfortunately still have the same problems:

The following packages have unmet dependencies:
tvheadend : Depends: libdbus-1-3 (>= 1.9.14) but 1.6.18-0ubuntu4.4 is to be installed
Recommends: xmltv-util but it is not going to be installed
E: Unable to correct problems, you have held broken packages.

I'm trying to find a solution for the"E: Unable to correct problems, you have held broken packages." bit first..

You're welcome
Give this a try:
sudo apt-get install xmltv-util
sudo apt-get install libdbus-1-3
sudo apt-get install tvheadend

oops let me see, missed the "broken package"

sudo apt-get update
---Clean partial packages
sudo apt-get autoclean
---Clean apt cache
sudo apt-get clean
---Clean up unneeded dependencies
sudo apt-get autoremove
---If can identify the broken package this code will very forcefully remove it. Replace "package name" with the problem package, do not use the " ".
sudo dpkg --remove -force --force-remove-reinstreq "package name"

I've done both your suggestions, the first results in something like this:

*ubuntu:~$ sudo apt-get install libdbus-1-3
Reading package lists... Done
Building dependency tree
Reading state information... Done
libdbus-1-3 is already the newest version.
0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.
*ubuntu:~$ sudo apt-get install tvheadend
Reading package lists... Done
Building dependency tree
Reading state information... Done
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:

The following packages have unmet dependencies:
tvheadend : Depends: libdbus-1-3 (>= 1.9.14) but 1.6.18-0ubuntu4.4 is to be installed
E: Unable to correct problems, you have held broken packages.

can I uninstall somehow libdbus-1-3 and install it again?

The second has the following output:
(long list of updated/checked packages)
Reading package lists... Done
*ubuntu:~$ sudo apt-get autoclean
Reading package lists... Done
Building dependency tree
Reading state information... Done
*ubuntu:~$ sudo apt-get clean
*ubuntu:~$ sudo apt-get autoremove
Reading package lists... Done
Building dependency tree
Reading state information... Done
0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.
*ubuntu:~$

also, the /etc/apt/sources.list

contains the following line (i've added it):
deb https://dl.bintray.com/tvheadend/deb xenial stable

sudo apt remove --purge libdbus-1-3
That should complete remove libdbus
Then I would go in this order:
sudo apt-get autoclean
sudo apt-get clean
sudo apt-get update
sudo apt-get upgrade
sudo apt-get install xmltv-util
sudo apt-get install libdbus-1-3
sudo apt-get install tvheadend

Oops.. I think i've found the problem.
I'm on Ubuntu 14.04 and I thought I had 16.04. That could be a problem

That very well could be the issue,
you will need to change in the sources.list from xenial to trusty.

Then run:
sudo apt-get autoclean
sudo apt-get clean
sudo apt-get update
sudo apt-get install tvheadend

Yes, worked without problems once I've synchronised the OS and the TVH version.
Thank you for your help.