John,
I've done this several times using the directions found here:
https://www.zen-cart.com/tutorials/i...hp?article=100

The gotchas are the Config.php files in includes and admin/includes. You have to make sure they are not overwritten when you upload your files from the old server.

Don't ignore the installation step (1.) as it is important. On one move I tried to just create a database upload my old one, upload the files from my old server via ftp (notice I skipped step 1.) and low and behold it didn't work. Follow the steps and you'll be fine.