1. Test the computer first. Take it out of the car and try it or take a monitor that you know works and plug it into the computer to see if it is working.
2. If that works, make sure the monitor is getting power. Use a digital multimeter to measure the power being supplied to the monitor via the power cable, which should be separate from the vga cable.
3. Test the monitor by connecting the (now confirmed) working computer, or a spare laptop to the monitor.
4. Find out what that last button does. It probably powers the monitor or acts to cut the signal to the computer so you can keep it from starting up if you valet park the car.
5. Use punctuation in your posts. My eyes glazed by the time I got to the end of it.