Hi
You can try this... This post was on the Adobe Forum.
I tried all solutions but one posted in adobe support. I am local administrator but IE security settings are set by group policies and buttons in tools security setting are grayed out.
After three days with "The ActiveX control for Flash Player could not be registered" message I tried registering the activeX control manually.
Bingo! that made the trick.
So open a DOS window, type "regsvr32.exe C:\WINDOWS\system32\Macromed\Flash\Flash10d.ocx" -first check if this directory exists and contains the Flash10d.ocx (no quotes needed) and you should receive a confirmation that it registered correctly.
I must say that I've tried so many ways that I cannot repeat...