In looking at the code on that page I don't think that "Support Us" button is in an HTML module (this is why when you login and go into edit mode you're not able to edit it). It may be coded into the actual skin/theme of the site or the skin/theme of this particular page.  

In order to change the link you could override the href property of the link via jQuery or you could try to find the skin/theme and update the link there... if in fact the link is hard coded into the theme/skin.

So how do you find the skin files...?
I'm not sure what version of DNN you are running, but you should be able to find a Page Settings area in the Edit bar. Then find the Page Appearance tab or section of the page properties. This should tell you what skin is being used. If you it says "none specified" then that means that the page is inheriting the skin/theme that is set in the global site settings. If this is the case then go to Admin > Site Settings > (Basic tab) Appearance and you will see the global site skin file being used.

Once you figure out which skin file is being used then you can look into your DNN instance's folder structure (usually located at YOURSITE/Portals/_default/Skins) for that specific file. If you have access to the server you can just navigate through your folder explorer to get there... then just open the .ASCX file that is being used and update the link accordingly.

Hope this helps..

When you say you went into the "File Manager" did you do this locally on the server or did you do it through the DNN File Manager? The reason I ask is because the DNN File Manager will not show you the .ascx files out of the box even though the files are present. They are not shown because the .ascx file type is not in the "allowed for upload" file extension settings list so DNN doesn't show them. It's a way DNN is protecting you from having malicious code uploaded into your site. If your site has a skin, and it's an older version of DNN, then it has to have a .ascx file being referenced. 

Also regarding screenshots, if you can't upload yet you can always download Jing (https://www.techsmith.com/jing.html) - it's free and then you can create a screenshot and upload it to their servers and then just reference it from here.

And speaking of Jing & the situation at hand ... I've posted a screenshot to Jing showing you my skin/theme file as it looks from within the DNN File Manager vs. how it looks locally on my screen. (Be sure to go full size on the image) - http://screencast.com/t/CVBgWSGznDcu - notice how the local folder explorer on the right includes the .ascx files