Have you a manual gear box? If yes when you use a skreem set from a automatic transnission the car will not start because it missed the signal, that the shifter is in p or n.
I think the company in the UK is Precission ECU? Yes the can modify your ECU, so that it works without skreem, but I think they will solder a module into the ECU what's handled the immobilizer function. I could also build such a module and there are some companies who sell this modules for the SLK.
You could check with the multimeter if the skreem and ECU gets power +12V and switched +12V. If you also have a oscilloscope you could check if the can bus works, the 2 wire white plug of the skreem, Without can bus the skreem can't immobilize the ECU.
Here is a cheap oscilloscope what is ok for most tasks on the car also checking the can-bus: ebay Ozi
And here is a youtube video how to check the can-bus with a oscilloscope: