I went to go install Lightroom 4 on Windows 8 and the funniest thing happened. After installing Lightroom 4 on Windows 8 the program would start, if you hovered your mouse over the Lightroom 4 icon the program would look like it was running. The program would seem to stay minimized on the start menu and would never open up.
Because of this flaw, I could never enter the serial number so that I could run Lightroom.
To fix this issue the best thing to do is locate the lightroom program and edit the shortcut located in this folder:
C:\ProgramData\Microsoft\Windows\Start Menu\Programs\Adobe Photoshop Lightroom 4.2
Right click the shortcut and click properties. Click the compatibility tab and and make sure the program is run in Windows 7 compatibility mode.
Hit Apply and Ok. You should now be able to actually see the application and enter the serial.