If you’ve pasted what is in the HTML there on CodePen: open the HTML page you’ve created in a browser, open the browser console. Is there an error? If so, what does it say?
Yep, shouldn’t need anything else. Babel is a tool to convert JavaScript code to JavaScript code (you have something using syntax that won’t work in a browser you want to run your code in → put it into Babel → get code that will run). There are very few reasons for putting it into a website. It’s almost exclusively used during development: converting code live is slow and uses a lot of resources. CodePen does have the option to use it, but none of the code you have would need it anyway afaics.
There is definitely nothing in the Codepen code that requires Babel and it wouldn’t work on Codepen (without Babel) if you did need it.
If you add Babel to the Codepen and view the compiled code (down arrow on the top right > View Compiled JS) you can see all it does is some formatting.
Use the browser console, see what errors it is throwing. Normally if something is missing, or you’re calling something incorrectly, it will tell you.
I just did that and nothing is getting thrown in the console.
So when I use the <script src='./index.js'></script> it loads the page with random color and random quote, but when I click on the new quote button it isn’t working.
I then add <script type="text/babel" src='./index.js'></script> and everything works fine. Console never logs any problem in both of the cases.