if your spending $300 on the monitor and wiring, $200 isn't much but you could get Intel® Desktop Board D201GLY for $60 here, cheaper if you search. M2-ATX for $90, that Leaves $50 for a HD and RAM. Maybe eBay for a used laptop HD or ask around I'm sure a friend should have an old desktop HD you could have. That would do you with the exception of internet. Hopefully you have a cell phone and plan you can use. In which case it wouldn't cost you anything.
An inverter isn't a bad way to go, I used one for years, but a DC-DC PSU is a lot nicer. Specially with a shutdown controller. I have the M2-ATX and it works pretty good. They are $90 and if you figure out how much an inverter, wiring, some kind of shut down controller, etc you'd probably be pretty close to that $90.