|From what you said I am not clear whether Flash was previously working on both IE and Firefox, or what happened to each one when you tried the website video.|
Delete all Flash download files that you have obtained. Now try getting the Adobe flash download on each browser that you have running, one at a time.
For each browser make absolutely certain that you know where it saves the download file. When you have done one, delete that downloaded file then do the next browser - there are variations.
Although you have posted this in the Hardware forum I doubt very much that it is a hardware issue.
Always pop back and let us know the outcome - thanks