I'm not entirely sure it is really that difficult to prove Car 4 is at fault. Car 1 can prove Car 2 caused the damage/injury to his vehicle, however, Car 2 will disprove negligence on account of being stationary behind Car 1. In fact, it will be Car 1's evidence that Car 2 came to a stop and was stationary, so Car 1 will only prove the damage element of a negligence claim, the duty and breach elements will be disproved on Car 1's own evidence in witnessing Car 2 come to a stop behind him.
I believe impact speed is at issue in what is referred to as a "conga line" vehicle accident, which makes Car 4 the likely negligent party.
In answering the OP's thread question -- it is Car 4. Car 4 was reckless and, therefore, negligent to be driving so fast that the impact speed would affect a total of three vehicles in front. In rejecting Car 1's letter as to liability for the damage/injury, Car 4 must realise that it is enough for Car 1 to establish the threshold issue of negligence.
Rod, Car 2 may get the chance to claim their damages, however in such self-represented matters time and inconvenience come into play and relying on other people to solve problems diligently and in a timely manner can often be at the detriment of people such as Car 1. And you know what Insurance Company 1234 would do in such a case if all drivers held their policies with them?
In conclusion: I agree with Ponala, start with a Letter of Demand addressed to Car 4, but if it goes to court sue all three vehicles and see where the chips may fall. As Car 1, you are seeking a civil remedy for the damage/injury to your vehicle/self. The contribution is for the magistrate to determine.