Roxxor, are you running Windows XP or Windows 2000? If you are, then the 60hz thing is the problem with the OS and not Half-Life or CS. Under Win2k and WinXP, the default refresh rate for OpenGL games are 60hz (the "safest" refresh rate for 2K and XP to display in 3D, as the OS determines). With Win98/ME, this isn't the case and the OS chooses the "highest" monitor supported refresh rate for 3D anything.
What you'll need to do is adjust the registry to allow your monitor to refresh at a higher rate than 60hz. Try
R E A D I N G the FAQs here, in the General Forums and from Google.com, they'll tell you what you need to fix it. With an Nvidia card, visit
http://www.planetquake.com/ztn for the tool that'll fix your Nvidia card easily.
If you only read the FAQ first (or searched for this topic, its been asked SO MANY times), you wouldn't have needed to post.
vash