There is a bug on MAMP 4.1.1. (At least on windows that I encountered). Use a previous (or next version if out already).

Using version 4.1.1, The Apache Server comes on, then MySQL, and then the Apache Server goes out. I tried changing Apache ports before trying a previous version (4.1)

Check the current version and download
https://www.mamp.info/en/downloads/

Or use this direct link to download 4.1 for Windows

MAMP

MAMP is a free, local server environment that can be installed under macOS and Windows with just a few clicks. MAMP provides all the tools you need to run a local web server with php (Remember LAMP?)

You can even run WordPress locally for testing or development purposes. With the help of local DNS server NAMO, you can even easily test your projects on mobile devices. It doesn’t matter if you prefer Apache or Nginx or if you want to work with PHP, Python, Perl or Ruby.

MAMP apache server not running