If your car is an auto, the black tube may be a cable/vacuum line that locks/unlocks the key in the cylinder unless it's in park. From the sound of it, you either don't have the immobilizer properly bypassed, or you're just engaging the starter, not actually putting all the car's systems to "on".
Honestly you'd be better off picking up a proper remote starter, even a used one. Junkyards where I am have tons in the cars, that's all you need (no need to find a matching keyfob).
Every remote starter I've installed or worked on has a input pin, when grounded or connected to 12v (depends on the model) will cause the remote starter to go through it's starting sequence.
You don't even really need an arduino for that then, and you'll be using a proven rugged solution.
Remote starters go on sale in stores here for $30 new, and used ones can be even cheaper. Sure it's nice to make things yourself but I don't think it's worth it for a remote starting system. If the arduino screws up and engages the starter at the wrong time, that will be costly.