When did this behavior begin? I see you're running v7.6.2, and I'm sure you'd have noticed this issue from when you installed it (it was released on September 18th, 2018). Has this only started with the change of webhosts? Do they have a complete backup of your webspace prior to the migration to GoDaddy's servers?
I'm sure Isaac meant no disrespect, but we've had numerous issues with GoDaddy over the years and I'm not really surprised at all that things aren't working well there; their plans start at $2.99, so he's just referencing the base pricing.
Just for reference, there are much larger sites running UBB.threads without problems, such as
24hourcampfire.com (7.6.0), and
KoPTalk (7.5.9); so I'm pretty sure this is either a server issue or an issue with the data that was migrated after your host was bought out.
The backup from prior to the migration might be whats needed if the database is corrupted. None of the queries have been changed in these scripts for at least 10 years, if they're not working now I'd suspect database corruption might be the culprit.