I didn't have GD2 and ImageMagic installed when I installed UBB. When I get them installed on the server is there anything I have to do with UBB to get UBB to recognize they are finally available or will UBB automatically detect them?

GD is normally compiled with PHP, it'd be able to be used instantly when the setting is available, you'll just need to tell the UBB to use it.

ImageMagick however you'll need to tell the UBB where the convert and mogrify files are located once it's installed.

More on UBB and GD2.

I am pretty close to asking for a refund.

I have GD2 installed. I did a fresh NEW install and Gallery sees that GD2 is there, however it is not shown as available in the following:

Use this Graphics Library for CAPTCHAs:
It appears you do not have access to GD2 or Imagemagick.

Maybe if it was installed after the fact you need to reboot the server.
But anyway you can goto the ubb control panel.
Control Panel » PHP Info
All it does is run phpinfo for you.
If you scroll down or search for GD you will see if it is really enabled.
This is not a fancy screen print but it should look something like:
gd
GD Support enabled
GD Version bundled (2.0.34 compatible)
FreeType Support enabled
FreeType Linkage with freetype
FreeType Version 2.2.1
GIF Read Support enabled
GIF Create Support enabled
JPG Support enabled
PNG Support enabled
WBMP Support enabled
XPM Support enabled
XBM Support enabled

Go in and just "submit" the gallery settings page (while GD2 is selected) and see if that fixes it.

I'm not sure why we're not just "assuming" GD2 is installed, since I've yet to see an instance where it isn't compiled with PHP, but for new installs there isn't a graphics library selected by default, which is why the graphics library option isn't showing anything in it.

In comes Ruben posting mere seconds before me

Back at ya!

By the way I had said I did a clean NEW Install after installing GD@ and Imagemagic

This is what it says in pgp info

GD Support enabled
GD Version bundled (2.0.34 compatible)
GIF Read Support enabled
GIF Create Support enabled
JPG Support enabled
PNG Support enabled
WBMP Support enabled
XPM Support enabled
XBM Support enabled

Did that just now for you and there is no change.

For example for captcha to work you must have:
GD2 with FreeType to be available to PHP.

Not knowing how you got gd2 installed. It looks like you need to check the GD2 settings again.
Since you did not provide a line item for that on your statement from phpinfo.

You must have missed some steps installing GD2

Bear in mind like Gizmo stated. Most all sites have GD2 pre-installed by there host so it is not a issue.
Usually it is ImageMagick that people try to use which is not installed and even then they don't know the paths.