Thats all a little strange!
One helping thing would be to find out if its actually the flash software itself or IE that the problem is with.
Go to this test site now and see if the software works,the flash section part normally takes a min or two if nothing happens at first:http://www.adobe.com/shockwave/welcome/
Im also interested to know if you have Shockwave Player installed also? If not,then install it,and any updates that are available.
Also,do you have an ''Add-Blocker'' as part of your anti-virus or spyware software and is it turned on? If you have and it is turned on,turn it off and try to see if that helps, normally add blockers will prevent software,like games and video loading on web sites because it recognises them as adds.
Some Internet Utilities, such as Norton Internet Utilities, perform functions similar to a firewall and may restrict viewing of ActiveX controls. You need to ensure that your firewall or utility settings are set to allow ActiveX controls or you will not be able to view Flash movies in Internet Explorer.
I found these instructions below from macromedia themselves,try them:Internet Explorer ActiveX settings
Although your browser security settings should be chosen by you or your system Administrator, the 'Medium: Default Level' will allow you to view Macromedia Flash content. For any Custom Level, ensure that both "Download Signed ActiveX controls" and "Run ActiveX controls and plug-ins" are not disabled. (Enable or Prompt will work).
To view your Security Level do the following:
1. Open Internet Explorer.
2. Choose Tools then Internet Options.
3. Select the Security tab.
4. Choose Internet.
5. Ensure that "Download Signed ActiveX controls" and "Run ActiveX controls and plug-ins" are not disabled.
If you are having trouble installing make certain that your Internet Explorer security level is not set to High or at a custom level which does not allow viewing of ActiveX controls.
I hope this helps,if not it may be an uninstall of the FlashPlayer and download and older version if the flash worked before,or,an updated version of IE, which version are you using incidently? I know Microsoft has just released a beta version of IE7,you can read more about it browsing the Bleeping Computer forums and see what others make of it,you may want to consider downloading it and give it a go,but thats up to you. Again let me know what happens as soon as you can!