These instructions assume the problem is not caused by a non-Adobe plugin for Flash, which in your case, given what you said, seems like a reasonable assumption.
First, completely remove the flash player by running this command in a Terminal window (Ctrl+Alt+T):
sudo apt-get purge adobe-flash\* flashplugin\*
Now, you should also remove all user-specific files created by Adobe Flash (and other Adobe software) before, which may be causing the problem:
mv ~/.adobe ~/.adobe.old
mv ~/.macromedia ~/.macromedia.old
Actually, those commands don't remove anything--they just rename the folders so Adobe Flash won't use them anymore. However, you can feel free to remove them afterwards.
Then install Adobe Flash. You can do it in the Software Center or with:
sudo apt-get update
sudo apt-get install flashplugin-installer
You have a 32-bit system so whether you install
adobe-flashplugin doesn't matter, but if you had a 64-bit system then it would be better for you to use the
adobe-flashplugin package. The
flashplugin-installer package only provides the 32-bit version of the plugin. (I'm providing command-line instructions for
flashplugin-installer rather than
adobe-flashplugin only because you might not have the software source for
adobe-flashplugin--the partner repository--enabled.) By the way, some instructions say to install
flashplugin-nonfree--that is equivalent to installing
Since it doesn't work in either Firefox or Chrome, clearing user-specific browser files is probably unnecessary. However, if the above method does not work, you should see if the problem occurs in the guest account (or any other user account--you could even create a new account to test). If the problem did turn out to be user-account-specific, then you'd want to clear browser-specific files to see if that would solve the problem.