It's quite possible that the problem could be data execution prevention stopping CS1.6 from running at all. Tried installing CS Condition Zero on my machine, and it crashed to desktop every time I went to start a game. I added it to the exceptions list for data execution prevention and voila! -it worked. It can be found by right-clicking Computer, select Advanced System Settings on the left, then Performance Settings and clicking the data execution prevention tab. It may be set to "Turn on DEP for windows programs and services only". Try selecting the other option (turn on DEP for all programs and services except those I select), and add ALL the programs you want to use to the exception list (a pain, but worked for me!).
CS1.6 will run with any version of DirectX with differing results. I have it set to DirectX11 (seems to run better for me)! It could also be blocked by Windows Firewall (open Start menu, type "firewall" and add CS1.6 to the list (private, not public). Hope this helps.
If you get it working and have any other problems (lag, high ping, etc,.), post a reply here and I will try to follow up.