To just start your game, you can use the Half-Life launcher ( default path C:\Program Files\Valve\Half-Life\hl.exe ) and in the game itself select Change Game, choose Counter - Strike and click OK. However, there is another thing that you can do. Right click on desktop -> New -> Shortcut -> select hl.exe file ( you need to navigate to the location where you installed the game ) and click OK. After this, right click on the new shortcut that you created, go to Shortcut tab, and in target field add
-game cstrike ( should be something like this
"C:\Program Files\Valve\Half-Life\hl.exe" -game cstrike.
This should fix your problem.