I have same problem like most of you. It's pretty strange for me because it's first GOG game with running difficulties. I check compatibility mode, resolution, all your suggestions.
Even switch off some of running tasks, also I don't have any of Logitech products. Any idea guys?
*UPDATE*
In my case help when I put it on the DEP exception list. (System Properties -> Advanced -> Performance -> Data Execution Prevention).
*UPDATE 2*
OK. It helps but only ONCE. Now still it doesn't work.
*UPDATE 3*
Finally I run it, the best solution was that one from another topic:
I solved this problem on my windows 8.1 computer by going into task manager, going to details, right clicking on KoDP and click on analyze wait chain. then I ended any processes in that wait chain and it start to work fine. I hope this works for everyone else!
That's good advice, just one more thing: this function is also available on Windows 7, just not in task manager. If you're using W7, use
Resource Monitor instead.