Try uninstalling it using http://helpx.adobe.com/flash-player/kb/uninstall-flash-player-mac-os.html
I am having exactly the same issue. I use OSX 10.8.4 on my imac 3.06 GHz Intel Core 2 Duo. Safari is 6.0.5. I've tried uninstall and reinstall. I also deleted flash player files from Library before reinstalling it. Repeated this procesures several times. None of it worked. The installation process seems to end successfully, at least I get the message saying it was installed, but it doesn't work and sure enough, when I check on the adobe site, the flash player screen remains blank.
I would appreciate it if you have any other suggestions other than just uninstall and reinstall. I can't run the e-learning session without flash player, and it's quite frustrating...
And, it seems there are quite a few people having the same problem in the last few days from browsing through this help site. I wonder why.
I do not have enough Mac OS knowledge to help you any more with this. The only additional thing I can suggest is to check if the Shockwave Flash plugin is enabled in your browser.
[Hello from a fellow Tokyoite!]
I turned off the plugins and java script setting on safari, restarted safari then turned on both plugins and java script again, and it worked!!
Thank you so much for your advice.