Your registration attempt has been blocked. Reason: Already registered.

Your captcha is broken because CB is not publicly accessible. Joomla menu access permissions are blocking public access to the component endpoint used by CB AntiSpam for rendering captcha. Setting "Membership & Registration" under Menus > Community Builder to "Public" will resolve your issue. You said you changed this, but it's still set to "Registered" are you sure you're making changes on the correct site?

When did all of this change? I updated the site and now all of this has become an issue. Some of the Community Builder can't be left public as there are paid subscriptions that need to be handled by this. I'm at a loss as to how this needs to be set up now.

A public Joomla menu item to CBs profile page (you don't need to make all your menu items public) has always been mandatory, but wasn't really enforced. Joomla 4 change the routing behavior removing some legacy routing logic which caused this to become a problem now. Profile access permissions are adjusted in CB > Configuration > User Profile while plugin access permissions are configured in their respective plugins.

Thank you for explaining that to me, I appreciate you letting me know. It is getting closer but still have some issues with this upgrade. 
I was able to register now and get to the profile page, but there is no payment button. It is an offline payment option, this particular client doesn't want to offer online payments quite yet. 
What I am trying to do is set it so that as soon as they register, they are sent an email with a link to a registration area so they can choose courses for a conference. I thought I had it all set correctly on the back end to do that, but I only get a Cancel Payment and Membership option. 

I have also noted some issues on a few screens that stuff isn't displaying quite right. I can open a different ticket for that. I have been trying to add a screen shot of my issue in the ticket and it's not allowing me.

I was able to register now and get to the profile page, but there is no payment button. It is an offline payment option, this particular client doesn't want to offer online payments quite yet.
What I am trying to do is set it so that as soon as they register, they are sent an email with a link to a registration area so they can choose courses for a conference. I thought I had it all set correctly on the back end to do that, but I only get a Cancel Payment and Membership option.

That should just be a matter of including a link to CBs plans page in your registration email. It should be as follows.

index.php?option=com_comprofiler&task=pluginclass&plugin=cbpaidsubscriptions&do=displayplans

Note that's a non-SEO link though and it's recommended to create a Joomla menu item to the CBSubs plans page then providing that link in the email. You can do so by creating a menu item with a menu type of Community Builder > Plugin then simply select CB Paid Subscriptions from the plugin list.

Aside from that I'm unsure what you mean by it only showing cancel payment and membership option. You mean there's no payment gateway available at all? Be sure your payment gateway is properly published and set to Public access in CBSubs > Gateways.

I have also noted some issues on a few screens that stuff isn't displaying quite right. I can open a different ticket for that. I have been trying to add a screen shot of my issue in the ticket and it's not allowing me.

Please make a separate topic for each individual issue you may have. As for attaching images it should work fine as long as you're attaching a file directly. The copy/paste functionality Kunena provides does not work very well if you're trying to paste and image from clipboard.

I had to save the image as a .jpg. I had tried a .png but it wouldn't work.