We swapped our WordPress site over to a new host and did a migration from one server to the new server. After that migration was done, our forums are now showing on the menu that all post and users are there, but the users name is 'anonymous' and we can't make new post or see old post.
Propably something was wrong in your database move (import / export).
I'm pretty sure if you enable DEBUG.LOG of WP, it will be full of fatal errors.
You did incomplete migration. I think these three tables were not fully migrated and identical restored:
Maybe the red marked table prefixes are not correct or tables where not fully imported.
Also please navigate to Dashboard > Forums > Dashboard admin page and click on all Delete and Reset buttons in Forum Maintenance section.