There is really nothing to convert. A .bat file as well as a Powershell .PS1 script can execute a program.
C:\Windows\System32\whoami.exe /groups
That statement is valid in both .bat and .ps1.
If the program that you want to execute is stored on another machine then just point the .bat/.ps1 to it.
\\00.111.222.33\C$\mydir\dir\MyProgram.exe /job:runmyjob
Since you've referenced C$, the account that executes the script will need to have administrator access on the 00.111.222.33 machine.
The machine that you run the script on will copy the MyProgram.exe over the network and load and execute it on the local machine where the script is running.
If you want to have a script on one machine launch a program on another machine then you need to use invoke-command.
Invoke-Command -ComputerName 00.111.222.33 -ScriptBlock {
C:\mydir\dir\MyProgram.exe /job:runmyjob
}