Hello Fred.

You can make sure the Flash Reader plugin is installed by going into Tools > Add-ons > Plugins.

If your browser is displaying weird behavior, you may be having a problem with some extension that is hindering your Firefox's normal behavior. Have you tried disabling all extensions (just to check), to see if Firefox goes back to normal?

Your above posted plugins list shows that you have the Flash plugin installed and you write that the Adobe Flash test page is reporting that Flash is installed and working. So if websites report that Flash isn't working then something must be blocking Flash.

See Flash --- Start Firefox in Diagnose Firefox issues using Troubleshoot Mode to check if one of your add-ons is causing your problem (switch to the DEFAULT theme: Tools > Add-ons > Themes). See Troubleshoot extensions, themes and hardware acceleration issues to solve common Firefox problems and Troubleshoot issues with plugins like Flash or Java to fix common Firefox problems

and there are some websites that have film clips that just show up blank with firefox, but not with ie.