I am following the example video of adding input forms to the Server Connect control. When clicking submit, I get this error message in my browser from IIS:

405 - HTTP verb used to access this page is not allowed.
The page you are looking for cannot be displayed because an invalid method (HTTP verb) was used to attempt access.

It works correctly when using the other controls, and with classic asp.

Hi Chris,
It seems your IIS is not properly configured.
You can do this:
According to your description and error, I think the question might cause by you have not setup the limit of HTTP Verbs, please try to refer to the following steps,

Go to "Control Panel"-"Administrative Tools"-"Internet Information Services".
Expand the tree to "COMPUTERNAME"-"Web Sites"-"Default Web Site".
Right-click on "Default Web Site" and select "Properties". (Alternately, select "Default Web Site" and press Alt+Enter.)
Select the "Home Directory" tab.
Click the "Configuration" button.
From the "Mappings" tab, select the "Add" button.
Click the "Browse..." button, choose "Dynamic Link Libraries *.dll" from the "Files of Type" dropdown, and select c:\WINDOWS\System32\inetsrv\asp.dll.
Type ".html" (without quotes) in the "Extension" box.
Select the "Limit to:" radio button, and type in "GET, POST" (without quotes) in the box next to it.

10. Click the "OK" button and close all the dialogs. (If the "OK" button is greyed out, then make sure all the entries are correct and try clicking in the file name box.)

Also - when submitting the form, please open your Chrome console and see what exactly is being posted and also what is the exact response.

I don;t have anything like that. I don't know what version of IIS those instructions are referring to, But I'm running Server 2008R2. I did manage to find the mappings and added the *.html extension. Now when I submit the form I don't get an error message, but the form values are not saved in the data base and I get this error in the web console:
Uncaught TypeError: jQuery.dmxServerAction is not a function
(anonymous function) @ formtest1.html:103

Are you following the insert record tutorial or the adding form inputs to the Server Connect Globals? As the second one is not supposed to insert anything.
Please tell me what exactly do you see in the response tab of the chrome web tools, when you submit the form.

Well, both actually. I changed the mapping and that seemed to get me past the error, so I proceeded to the insert record tutorial. When I click submit, the page refreshes but no data is added. When I pull up the console in Chrome, this is what I see:

Uncaught TypeError: jQuery.dmxServerAction is not a function
(anonymous function) @ formtest1.html:103

I checked all of our servers to see if maybe this one had an odd configuration, but all 6 of our IIS servers have the exact configuration as this one, and all run ASP.NET (2, 3.5, 4 and 4.5) classic asp and some PHP. They all run some of your asp server controls with the updater, etc. Are other people able to run this without issue on IIS server 2008R2 without issue?

What do you mean by: "When I click submit, the page refreshes" ?
The page isn't supposed to refresh if you are using this right. Are you sure you've bind the executor on form submit?

Still is not working for me. What I mean by the page refreshes, is that when I click the submit button, the form data clears out, and the list of data on the screen that shows what was supposed to be updated reloads, like there should be new data there, but it's not. I checked the database just to make sure. And yes, I made sure that I have checked the "On form submit" checkbox. Are there suggested IIS settings that you can share?

There are no any suggested settings actually.
It would be best if you can provide a link to your page, where we can check this:

I received your files and i see a problem with your form.
You've placed a submit button and you attached an onclick behavior to it ...
When you are using a submit button, you shouldn't use an onclick behavior, as the behavior won't run, and the page will just refresh.
As it is explained in the video tutorials, that you follow, you must select the "On submit" checkbox, when you setup your server action executor. Then it will run when you pres the submit button and the page won't refresh like that. So please remove the onclick behavior from your submit button and edit your server action executor like i explained.

Also: please remove the <script src="js/jquery-1.11.2.min.js"></script> include at the end of your page ... the jquery is already included in the head tags of your page.