Well I figured out the issue preventing the install of Chocolatey.
It was because these specific machines are on an off-internet network, and were also NOT connecting through a proxy server.
After applying a .reg file to set the computer to use the proxy server, Chocolatey installed, and therefore salt-minion installed, too, (after whitelisting .saltstack.com on the proxy servers). I entered a pssession on the machine and seen that Chocolatey installs salt-minion from the saltstack.com repo. All is well now, so long as off-internet computers are using a proxy server.
Script log file:
2018-03-23 11:18:52 Checking for Salt Minion process.
2018-03-23 11:18:52 Salt Minion is NOT running. Attempting to start.
2018-03-23 11:18:52 Salt Minion executable is missing. Can't start.
2018-03-23 11:18:52 Salt Minion is still NOT running. Attempting to reinstall Salt Minion and Chocolatey.
2018-03-23 11:18:52 Checking for Salt Minion process after reinstall attempt.
2018-03-23 11:18:52 Salt Minion is still NOT running. Reinstall FAILED.
2018-03-23 11:18:52 Email sent to ****@****.com - Salt Minion reinstall FAILED on ****03
2018-03-23 11:18:52 Checking if Chocolatey is functional.
2018-03-23 11:18:52 Chocolatey is functional.
2018-03-23 11:23:50 Checking for Salt Minion process.
2018-03-23 11:23:50 Salt Minion is NOT running. Attempting to start.
2018-03-23 11:23:50 Salt Minion executable is missing. Can't start.
2018-03-23 11:23:50 Salt Minion is still NOT running. Attempting to reinstall Salt Minion and Chocolatey.
2018-03-23 11:23:50 Checking for Salt Minion process after reinstall attempt.
2018-03-23 11:23:50 Salt Minion is running. Reinstall successful.
2018-03-23 11:23:50 Email sent to ****@****.com - Salt Minion reinstall successful on ****03
2018-03-23 11:23:50 Checking if Chocolatey is functional.
2018-03-23 11:23:50 Chocolatey is functional.
However, I still would like to know how to have the Chocolatey installer append it's install status to a log file from my script.