$powershell path is set to "C:\powershell" at line 27. This is fine, but on line 82 $powershellpath is called as ".$powershellpath\$filename". Because the path at line 27 is absolute, a period preceding the $powershellpath is not required at 82. It actually causes an error:

Start-Process : This command cannot be executed due to the error: Unknown error (0x80041002).
At C:\users\Nathan Sosnovske\Documents\ps2to3.ps1:81 char:14

Start-Process <<<< -FilePath ".$powershellpath\$filename" -ArgumentList /quiet
CategoryInfo : InvalidOperation: (:) [Start-Process], InvalidOperationException
FullyQualifiedErrorId : InvalidOperationException,Microsoft.PowerShell.Commands.StartProcessCommand
Removing the period on line 82 before $powershellpath fixes this error.

Must wait in order for script to be available

Debugging

Fixed

Using Start-Process

UpgradeToPS3.ps1 failed when tested with Ansible. Added logging output
to file C:\powershell\install.log.

assumed.

Will install PowerShell 3 if the machine has a lower version. WILL NOT
do anything if PowerShell 3 (or higher) is already installed.