So if it is a not compiled module you just have some code files into the App_Code path of your dnn root. Those file have to included into the manifest file, and on install the web.config file must be modified with adding the module path of the app_code.  If this is missing the installer can not add your module.

I don't think that I can found a solution for you without to see what are all the module Project files and see what files are added to the module.zip file and how the manifest Content is.

What is the different between the DNN instances where the module already runs and the new instance?

It is also possible. that a newer Version of DNN have any changed that Need a modification of your module.