I am having difficulty downloading the game Total Anhilation. It tells me "Installation failed, disk access proplem" I've tried to do the different download methiods but I keep getting the same thing.

Have you tried asking in the game's own topic?
https://www.gog.com/forum/total_annihilation_series#1543537812

Otherwise:
- do you have enough space on your disc?
- have you tried installing as administrator?
- do you have legitimation to install programs on named computer?

It is a brand new computer, plenty of space on the HD. I am the owner and thus the administrator so permissions is not an issue.

Goto the website and login. Goto your account, find the game in question in games. Click the download offline installers. You will see at least 1 file, maybe more. Download the exe and then bin files. Wait till they have fully downloaded into the same folder. Double click the exe. In options set to install to c:/mygames or something like that, outside the windows folders. Voila. You may need to enable directplay too. And you can keep the downloaded installed files on a backup drive for the future - this is the only reason to shop here as you get to keep the game.

Thank you, I was able to get it figured out and working.