Install winlogbeat on windows server 2003 without powershell

The New-Service powershell cmdlet is used by the script to create the winlogbeat service. You could try to install Powershell 2.0 and see if the script works. Microsoft's website doesn't have much information on Powershell 2.0 so I don't know if New-Service is present in the version.

Another option might be to use sc.exe to create the winlogbeat service. See https://support.microsoft.com/en-us/help/251192/how-to-create-a-windows-service-by-using-sc-exe