The solution is obvious. For the top track, Number each person that would be killed, and add a device to the front of the trolley such for each enumerated person reached, it will save them if the corresponding Turing Machine in standard enumeration halts. This has become an instance of the halting problem and thus the trolley cannot run.

Similarly, the bottom rail is even easier. Add a device that will save the person that is represented by the real number whose value can be decoded as the set of turing machines that halt. Once again we have an instance of the halting problem and, once again, the trolley cannot run.