Ok, I run with a GeForce2-32meg card. I've heard it was better then some of the later cards but let's see what we can do with your TNT card. Don't expect much, the minimum spec is a P3 900 Mhz, GeForce 2 etc. but maybe you'll be able to fly offline and look at the scenary.
Error 3 is a video error and error 5 is a sound card issue if I remember right so you have a video problem. Try to match your desktop video settings to what you want to try in AH2. Remove the video7.cfg file from the settings folder in AH2 and relaunch AH2. The video settings dialog box will appear so AH2 can rebuild the video7.cfg file and you can try the setting you used to setup your desktop. Keep track of which settings you've tried so you don't waste time repeating them. Once you get in, AH2 should set the remaining in-game video settings for you but you might tweak them down to fly and up to see better.
If you are comfortable using note pad to edit the video7 file directly you can but this is going to be safer for you and less error prone.
I don't have anything to add except good luck and I hope it works for you.