Thought this would be a topic to bring up to the front page for those who are having trouble to install the Diablo III Beta client. Blizzard is aware and has come up with a workaround. Here is a quote from Vasadan (QA Team):

Vasadan: We currently have three bugs with installing and streaming, all of which will be fixed in a coming Beta patch. If you do not fully download the game before playing, you will be stuck at a Loading screen. You are actually downloading the rest of the game, but to the user it looks like a hardlock or crash.

The current workarounds for these issues are:
When downloading the game, wait for it to completely download. This means waiting for the game to get to the green bar and allow it to optimize. When the bar turns dark green and is no longer moving, you should be able to play with no issues.
Fully uninstall and reinstall the game. After reinstalling, follow the steps for the first work around.

Again, this will be fixed in a future patch. — source