I was having the same issue, with about 9 hours of research and playing around on my new laptop I finally got it running. The solution was the stupid ATI Catalyst Control Center. If you have it installed and it isn't version 10.8, it won't let the game pickup on your video card (Which is needed to do the initial install of the beta client).
The only way I was able to get this working was to go to the ATI site and download the 10.8 complete version, uninstall ATI Catalyst Control Center completely from computer (Drives and all folders that the uninstall don't get are also important to remove, I used a program called "DriveSweeper") After uninstalling, restart computer, install new ATI with new Drivers, restart the computer, download the beta client (I downloaded the torrent from Demonoid.com and just unzipped it and moved it to my "Program Files (x86)" folder. Download takes a while due to the 4.6 Gb file.), Restart computer, hit the Beta exe. and BAM! it started to download all the patches. If the patch download freezes, just restart the Beta exe., sometimes the patch download will seem like it isn't working and then all of a sudden 175Kb/sec.
Hope this helps, it seems like most Windows 7 (64bit) computers with ATI cards are having this problem.
Edit: Forgot to put a space between "Restart" and "the", was bugging me... lol