Ive had a nightmare getting this game all set up.
The download worked fine, ran the install and that worked fine, entered the code all ok.
Then windows live started and it all went crazy, claiming i wasnt connected to the internet. Then the game kept crashing, then it kept saying i had no profile even though i used my xbox one etc etc.
Eventually got it working only to find the game has numerous bugs connected with AERO and windows 7. The game will also crash if you try to alter the V-Synch settings. You have to reboot your pc as it hard locks the machine.
Its best to run the game from a shortcut and use the compatibity settings on the shortcut to turn AERO off (select disable desktop composition ) and also run it as administrator... and now all seems happy. Phew...
That's a lot of hassle. On my windows 7, 64bit machine I never had anything like that.
When i first tried to run batman AA (another GFWL game), I had the same conenction problems you describe initially. But I shut the game down, and installed the GFWL client manually, outside the game, and then all was well.
I installed Dirt 2 after that, and didn't have the problem - probably because GFWL was already set up.
When playing dirt 2, and other modern graphically demanding games, I did have an aero-related problem, but I wouldnt call it a bug. It's actually a feature, if an irritating one. When playing, it would popup and ask if you want to disable aero, but as you found, you can bypass that by going into a program's compatibility settings and clicking "disable desktop composition"
I never had to set "run as administrator".
You can set those compatibility settings directly on the games launching exe file, rather than a shortcut. I do this, in case I need to create a new shortcut in a different place.