With Mugur's help, we finally installed Campsite 2.2.1 and everything is working perfectly except the HTMLArea. When we try to edit an article, we get a blank bar with no buttons. If we pressed CTRL+B, the text becomes bold, which means that the functionality of the HTMLArea is present, but with no visible buttons.
Another thing that I noticed, Campsite installs HTMLArea documentation and demos along with it under http://server/javascript/htmlarea/. I'm not sure if that serves any purpose or it was left by mistake.
So, let's find out why the buttons are shy and don't want to show up?