Power over ethernet questions

To sort of give a brief example of what I am wanting to set up, I (with the help of some others) build custom cars trucks and other automotive work. We have a project that is, and has been a big part of the work. I am wanting to set up an entire touchscreen, and wireless control system for this custom truck and be able to control everything via the car computer with touchscreen, and on a phone or tablet. I have been looking for this answer and have come up with no results. This is my question, can i run the board, hooked up on a power over ethernet connection, to a router, and have the router not hooked to the internet, but have it able to hook up and sync with the phone and tablet to still be able to control the program on the truck? The system I have in mind is the arduino board, with a 16 relay modual, hooked to the car computer, and controlled off of the touch screen mounted in the center, and with a laser keyboard. If you have any tips or a better idea that would still allow me to have wireless control of the relay modual. If you are able to help me out i would greatly appreciate it.

I fear your brief is too vague and unfocused to get many replies. What sort of power over Ethernet? Using the unused ways? Common mode?

This is my question, can i run the board, hooked up on a power over ethernet connection, to a router, and have the router not hooked to the internet,

Yes, you can use a 10BaseT connection and use the other unused wires in the cat 5 ethernet cable for power.

i dont think you need POE, you need an app. saw this online but do your research: http://www.myn3rd.com/