I have found that the easiest way to ‘move’ a blog is to clone it with WP Clone plugin (https://wordpress.org/plugins/wp-clone-by-wp-academy/ ).
You install it on the source system and do a backup. Then you install it on the target system and restore the backup. Ta-da! Both systems are exactly the same.
Although you can do it manually, it requires a lot more steps (and a hope that you don’t screw up the database). I’ve found WP Clone to be the easiest and fastest way; there are other ‘clone’ plugins also available.
Since the new site is not working, you might find it easier to start over with the WP Clone plugin. It will transfer all media, adjust URLs, etc.
It is probable that the media files are there, but the URLs associated with each media file in the database are pointing to the old place. You can fix that with some phpMyAdmin commands, but that’s a lot of work – and prone to error.
That’s why I let WP Clone do all the work. (and partly because I am too lazy to do all the work…)