There are two different installers: one for Internet Explorer, and one for Firefox and other browsers. You need to download and run both of them.
Download them from http://forums.adobe.com/thread/909550
If you don't know what Windows edition you have (32-bit or 64-bit), then run the installer from http://get.adobe.com/flashplayer/
I tried the one at from http://get.adobe.com/flashplayer/. It installed and said I was running Internet explorer. I got a dark screen when I tried a video.
I started the 64bit installer but got the message that the file is not compatible.
I’ll try rebooting