I have Windows 64 Home (SP1) and IE10. After I attempt to install Adobe Flash, I get a black screen on the IE Adobe page. On the video settings for a video window, I hear the sound, but the config shows Plug-In NOT INSTALLED. I see the installed files in the lower-level WINDOWS folder.
This sounds similar to this problem: http://forums.adobe.com/message/5215494. There is solution available in the same page. Please go through and try fixing the issue.
Hope the above helps.
If you only use IE, you don't need the plugin.
I agree with Prabhu that it could be a graphics driver conflict.