Search feature doesn't find anything

I have a site set up with the Music State template, but when I try to use the search function it never finds anything.

F.ex. : http://musichobo.com/index.php/search

On that website I have a button (on the front page) called Heavy Metal. When I search for "Heavy Metal" I get no results. I've tried looking for other text on the website and I keep getting no results. Is it possible to configure the search function so that it actually finds stuff worth looking for like names of buttons or videos on the website?

Hi,
we didn't change of default Joomla behavior,
but I think you do not understand different between two Joomla search engines.
One - old, default should work always
Second, Smart Search - request much more work and settings from back-end.
More info you will find on YouTube or guides in internet

p.s.

I tried both the "Smart Search" menu item type and the "Search" menu item type, those are the only two I can see in the menu item type list.

Upon further testing, it seems that they can find things inside of articles but not Custom HTML module. How do I configure it so that it also checks text inside Custom HTML modules, such as the one on the front page?

I'm not sure if Joomla can also search on modules.
But those questions you should ask on official Joomla forum, not here, I hope that you understand why.