Those games you mention are all OpenGL, so your issues may be related to your OpenGL settings in your drivers. Maybe not, I'm not exactly sure about this. First of all, try the following: Find the Half-Life's executable and right-click on it and access its properties, and make it run with Administrator Privileges, and if that doesn't work, leave that enabled and just add a compatibility mode with Windows XP SP2. That may help run the Half-Life-based games (the ones using H-L's engine, such as TFC and OPF).
Same thing goes for Quake, just locate the main executable in the installation directory and try the same thing. If all of that doesn't work then maybe it's related to your OGL settings, but if you're using an NVIDIA graphics card you'll need to use a third party program like RivaTuner to adjust OGL settings since the default NVIDIA's control panel only allows adjustments for Direct3D settings.
And then there's the usual things to do like making sure that you're using the latest audio and video drivers, the latest motherboard BIOS and the latest chipset drivers.