My Witcher 1 enhanced didn't crash to desktop whenever I entered combat but it did occasionally more often than i liked, crashed at random moments to the desktop. I just learned to deal with it and saved often. This may seem drastic but i'd try reloading your operating system and installing the game and running then seeing if fixes things. You can at least isolate the problem from other programs, etc. causing issues.
If you do end up doing that and it crashes again at least you can start focusing on hardware, driver related problems on your laptop.
But before you go that route, do your basics.... update all of your drivers, run a hard drive diagnostics and check for errors, make sure your windows and related components are patched up to date, try disabling any unnecessary software/services/antivirus/firewall etc and try running the game.