It's quite likely that you already had Flash player on your PC (as most people do) but that it had stopped working. (That seems to happen quite a lot!). If so, a new installation is doomed to failure because your PC sees that the plug-in is already there.
The solution is to go to Add/Remove Programs (or to the equivalent location used in more recent versions of Windows) and uninstall 'Adobe Flash Player Plug-in'. Then download and install from here:
http://get.adobe.com/flashplayer/
Chris