Hi. I encountered this same issue with Tomb Raider Legend but then I discovered the weirdest thing.
After I initially installed the game I was able to play it fine right away, but the next day I started having these exact issues (game starts, minimizes, hangs). I went through all the DEP and virus settings rigamarole without any luck.
So I gave up and put all the settings back where they had been previously, then I walked away from the game for a couple of days. When I tried again after about 48 hours, it suddenly worked.
After fiddling around a little, I discovered that I could get the game to work by doing a cold start of my laptop. Not by selecting "restart" from the power menu, but by selecting "shut down", completely shutting it down, waiting a few minutes, then booting from scratch. When I did that, this problem went away and I was able to play the game.
This is strange, and I don't know if this is unique to me, but I wanted to toss it into this thread so it's out there and googlable in case it might help someone. I'm running the game on an MSI GT63 with Windows 10.
Hope everyone gets their issues resolved and has fun with the game.
Thanks.