Some tips to ensure you’re doing the installation properly and help you trouble shoot in case the problem persists.
To get proper installation for the IE, you need Administrator rights and you should accept all pop-ups and prompts, as per procedure described by Adobe. The installation is direct thru the IE, and at the end of a successful installation you should see the animation on the same page. Did you see this animation? You also get the message “Successfully Installed”.
http://get.adobe.com/flashplayer/
You can also see version information and you should have version 10,1,85,3 installed.
http://www.adobe.com/software/flash/about/
Like gbhall said, the procedure for Firefox is different from that for IE and involves first downloading the Flash player, closing Firefox and then installing it.
http://www.adobe.com/products/flashplayer/productinfo/instructions/
Adobe itself gives the following trouble shooting advice for Flash Player installation for Windows. If you still have problems, check it out.
http://kb2.adobe.com/cps/191/tn_19166.html
In particular, if Flash Player crashes Internet Explorer for Windows XP, Vista, the solution is given below.
http://kb2.adobe.com/cps/408/kb408620.html
Finally, if nothing works, try a new browser like Opera and install Flash player as per Firefox.