Remote control of third PC via video-conference?

I have a PC which controls a fabrication machine. On this machine-PC, no additional software can be installed and it cannot be connected to the internet. So, there is no way to install TeamViewer or something like that. Nevertheless, I would like to control this PC remotely. The remote control is basically limited to check the current screen and make a few mouse clicks here and there remotely. There are no time critical steps. If the keyboard could also be accessed this would be a nice add-on. So, getting the content of the PC screen seems to be relatively easy: I place a laptop with internet

Question by theozh on Super User, licensed CC BY-SA. We show a short excerpt and link to the original thread as credit.