It sounds like the index.swf file is getting information (other file names and where they are) from an XML file. And when it can't find the XML file or it contains an error, it fails to load. Thus some things are loading OK, but the things that it can't find or load for some reason hang up and you see the loading circle for those.
It seems like the XML problem would be something wrong server-side (the swf file can't get at the xml files OK). Yet if that's true, it seems that the site would be buggy for everyone, or if an intermittent problem it would be OK sometimes but not at other times for everyone, including you.
Have you tried emptying your browser's cache? Perhaps it's saved an out-dated version of a file and contains now non-existent information, or doesn't have some now existent information it needs (I have my browser set to empty the cache every time I close it, so I'm loading "fresh" files from your site when I visit it).
As for Joomla, you can try it for free at your own pace if you're up to installing it. If you download a free server to your computer (WAMP, XAMPP, XAMPPlite, easyPHP, etc) you can download Joomla (or something else like WordPress, etc.) to it.
For example, with XAMPPlite I would unzip Joomla in the htdocs folder. Then I click on xampp_start.exe to start the server. Then I open a browser and go to http://localhost/Joomla/ and there it is. When done, close the browser and click on xampp_stop.exe This way you can experiment at home offline when you want without needing to find a new host to learn things on. And once you're ready, you can find a new host and upload everything to it ready to go.
IMHO XAMMPlite was relatively easy to install (I used the exe file) http://www.apachefriends.org/en/xampp-windows.html#646 as I didn't need to make any changes to any Windows files or the registry like some other things I've installed needed. And it should be more than adequate for your needs.