Same thing happened to me, I had to send it in ultimately and it got a motherboard replacement. One thing you could try is to hold down right mouse to force an INtel GPU startup. I didn't think about that one until my PC was sent away but I think that could do something. Please keep us at least me informed as to whats going on and what happening. I'm curious to know because I had THE EXACT same issues and after calling alienware they just told me to ship it in and they replaced the MOBO for me. I tried moving this moving that doing this doing that, and pretty soon it wouldn't even show up anymore. I think it's the Cmos but be careful on moving the Cmos it has to be done in a particular way. This is a very Fussy Machine IMO, and requires a good amount of maintenance and knowledge to use, and again this was my first alienware. And this alienware got me HOOKED, all PC's from here on out are going to be alienwares, lol.
I don't want to scare you but I personally belive that the MOBO on this system won't last beyond 2 years. But.... I could be wrong, lol, just a hunch.