After I click the "Start New Game" button I get the screen saying that if you'd like to see the game completed to back it on kickstarter, then the game crashes.
Okay, if there's really no graphics card that would explain it. We're still to pick a minimum spec and while it is probably very low, every game needs some graphics processor to handle the visuals. You've probably an on-board built in GPU?
It might also potentially be the 4GB of memory, the game uses nearly 2GB so if there's a lot in use on your system already it would struggle to run. Again, we've not had chance to test it ourselves on a wider range of hardware but the minimum spec may end up being 8GB of memory rather than 4GB.