I will warn you, though. Clean out your GPU fans before you get started to be safe. This game will tax your graphics card and if you're not careful you can have an overheating problem. Take 5 minutes now, save a headache later. :)
I had this exact issue on my machine. I ended up setting both Neverwinter.exe and Neverwinter\Live\GameClient.exe to run as admin and now I am able to start the game.