Sprout forms internal server error after migration
It sounds like you're missing some necessary Sprout Forms files.  Maybe they weren't FTP/copied over to the new server properly or if you're deploying from Git, maybe there was a gitignore rule that they got caught up in.

If you enable devMode, you'll probably get an error message on the front-end.

Regardless, I'd grab a fresh copy of the plugin and replace the existing craft/plugins/sproutforms folder with the new one.