Like some this may or may not work for you but I will tell you what I finally did to enable my Open GL to work with Half Life (and mods) on Windows XP with a Nvidia card.
1.Made sure motherboard BIOS was current
2.Installed the VIA current drivers (4 in 1)
3.Installed Nvidia Display driver (current 44.03)
4. Used the Destroyer tool to clean the registry (also manually searched for old 3dfx keys that were in there and removed them as well)
5.The biggest step and the one some may have not thought about : Remove ANY file in the HALF life folder that shouldnt be in there.
I had some display DLL's that said opengl32 etc in the half life root folder. Upon removing them i tried the game. Open GL initialized properly and worked.
Be careful when doing this as you dont want to remove something critical. The best way I would suggest is to clean install half life.
First uninstall it THEN delete the remaining folder. Check the and clean the registry. Each time you change something test the game. It took me a month of doing things like this but this whole process only took me a few hours.
After I got it running i noticed that in opengl on this card it looked and scrolled GREAT but i maxed out at 60 fps.
This was corrected with the nvidia refresh rate fix tool. My monitor wont refresh faster than 85 so i had to take that and ride. 85 fps opengl is good for me.
Good luck and keep trying you WILL get it. Getting mad isnt gonna fix it.