I had been facing the similar problem in Windows 7 and got the below problems while running the android-studio shortcut from my start programs menu for the first time.
Solution : Run As Administrator
The problem was due to the write permission in Windows C:
drive and the Access is Denied
message is displayed. Running the program as administrator downloads all the necessary components and now I can start Android Studio IDE.
Update:
These permission issues doesn’t seem to exist in Android Studio latest versions(checked in 1.3.2 in Windows 10) and works without the “Run as administrator” commands. If you still have the problem with the old/latest versions then it might be your firewall and proxy issues. In that case check out the other answers.