When I open the game, I click on the Network button, and then it freezes for 15-20 seconds, then the network tab appears. Each click on a button has the same effect. And I cannot see the list of servers online/offline/compatible (it's empty).
Firstly try restarting your internet connection from the modem (usually called a router now). This often gives a new IP so can solve issues like this. If not then it could be something far worse.
Sounds like the problem I had, it started 2 months ago around the time of the froum DNS issue. The cause was my IP address range being blocked by the server centre that hosts the multiplayer listing server. If you cannot access this web page http://servers.simutrans.org/list
then there is a chance that your IP range has been blocked by the server centre for malicious activities (probably not your fault but others who share the same range). In my case the entire BT ISP was blocked so most of their owned IP address ranges assigned to customers were being blocked by a firewall at the server centre so could not use the listing server or access the SVN. It was solved by getting the IP ranges unblocked, however this is not automatic.
If your IP ranges are blocked then you will need to post which ISP you use and an example of the IP you are currently using. There is no guarantee you may ever be unblocked as if the ISP is still heavily involved with malicious activities it may not be viable for the address range to be unblocked. It also requires some administrative overhead so could take some time.
One can hack around it to some extent using TOR, a custom build and a custom written port tunnel. However I only recommend this for computer scientists since it is far from user friendly.
The game was not written to be multi-threaded and so freezes for I/O to occur. Since it cannot create a TCP connection to the multiplayer listing server the game freezes for several seconds while several connect and timeout cycles are attempted before the call finally returns with a connection failure. What should rather happen is that the game polls the internet module showing a "waiting for connection" message while remaining responsive, however my crude attempts at writing this resulted in crashes as the game uses too much share state.
If a proper multiplayer synchronization model is introduced (one which does not allow clients to run ahead of servers) then maybe proxy support could be added. This would allow the game to work directly with something like TOR to avoid such blocks at the expense of extremely bad latency.