I really appreciate your help.
I've checked if there is a gamestate.txt or a stats.bin but they are missing (maybe because I've never started this game before).
So I've tried to start the game without internet (pulled the cable from the LAN adapter).
Unfortunately I have the same issues
But I have noticed two things:
If I try to start the game through the shortcut on the desktop nothing happens but in the taskmanager appears the hl2.exe and revloader.exe.
They stay there for some time and then they disappear again.
I've also tried to start it with the -dxlevel 80 parameter.
After that I tried to start it this way:
"C:\Setti\Counter-Strike Source\hl2.exe" -game cstrike -steam -console -novid
It works but when I create a game/server it aborts with (sv_lan 0 is set):
CD Key authentication invalid for internet servers.