Ouchie on the price. Get a cheap PSU and inverter.
..."some way of" turning it on remotely? What do you think the way is that you're doing it in a normal case? Do the same thing. Switch for the inverter, then a momentary switch going to the mobo's power switch.
Edit: you really should have described the situation better. I only figured it out because my dad was looking into replacing his inverter and PSU with a PSU that takes 12v DC in, and Opus looked like a good solution.
...if you're building it from scratch, look into VIA. You can get small extremely efficient PSUs for the mini-ITX boards for like $50. Most are still 120v in, but your loss is then mostly on the inverter, not as much in the PSU (and the machine will be itsy bitsy).