If its" line of site" there's tons of info online about long range wifi. It can be as simple as using 2 old Dish Network dishes pointing at each other. You could have a slingbox on one end of a really long wifi network.
Although you mentioned 12v so I'm thinking there isn't any power right? And under $100? Maybe I don't have any ideas after all.
What about a cell phone with unlimited data? Skype?
A neighbor with wifi?
If your buying a new projector, buy more lumens than you will use. Running it in "Eco Mode" makes your bulb last 20-40% longer and reduces noise and heat.
Run the camera output into an old VHS recorder, then the channel 2,3 or 4 output into a big VHF antenna, at the far end another big VHF antenna.
Sure it's not technically legal, but just who would you interfere with?
This should work at 20 000 feet ( 4 miles) but not 20 kilometers (12 miles).