I must also be having some type of a script problem.

Could be. If you bring it up in firefox, go into Tools and click on Error Console. Scroll to the bottom and see if it's showing any errors.

Thinking out of the box on this there is also a issue if there are any extra files in the captcha folder other than what was installed from the original zip.
I had a similar problem two years ago. The ftp program I was using at the time wrote a log.txt file in the captcha folder and that broke it.
Just deleting the extra files that don't belong fixed it.

I already removed those extra files without any success, therefore, I will reload those files and see what happens after that.

I will do this first and see what it says.

This is the only message I am receiving in the Error Console:

Deprecated method document.getSelection() called. Please use window.getSelection() instead.

I haven't reloaded those files yet, however, I soon will be doing that.

By the way, I can see the image box showing the X in Interent Explorer, but can't see any image at all using Firefox.

Using IE, when I click on the X image, I see the reloading image arrow, but it continues to show the X image, however, I can't see the image or really do anything to reload it using Firefox.

I don't know if there is a setting in firefox to turn it on or off but it usually hides the old red x.
The reloading thing happened to me also with the extra files issue.