Ideally you would have the entire environment when it was running in version control, and build every version since to see where it broke.
You might have your code in version control, but perhaps not Emscripten itself. If you've updated Emscripten, this could lead to differences in behaviour. I would try going back to whatever version you used when it was running. Note that sometimes various cache directories survive an Emscripten version change, and might need to be cleared manually (I forgot which exactly).
The dependencies remaining could mean that you are trying to do something before Emscripten has loaded any other files it needs to, say files requested by --preload-file or --memory-init-file. Note that according to https://kripken.github.io/emscripten-site/docs/getting_started/FAQ.html#faq-when-safe-to-call-compiled-functions you should not try to run any Emscripten functions, until the C++ main function has run. To detect this, you can, for example, call your own Javascript function from main (there are other ways).
The fact this wasn't causing a problem before could have been something that seems quite unrelated: a change or update in the web browser, changing limits of concurrent downloads, or a change in the web server this is running from. You could look in the Network tab in the browser to see if anything leaps out at you as being different or suspicious.
However, as main isn't even reached, then it might not be that. I would try commenting out virtually all of your code, and make it so you have practically nothing but a hello-world program. Perhaps you don't have a correct setting in the Module object, or maybe the request for the memory initialization file is failing (you can check in the Network tab in the browser for that one). If your basic hello world program still isn't working, then you could post again, with its code, in a separate question.