The reason for the error should be visible in the error log. You can find it in your hosting area. If necessary, the support of your hosting can help you.
Alternatively, you could also enable debugging in WordPress. How to do this is described here: https://developer.wordpress.org/advanced-administration/debug/debug-wordpress/ – also here the support of your hosting can help you if necessary to edit the file accordingly.
In both cases you should be able to see what the cause is in the logfile.
This looks like a hosting access issue rather than just a WordPress error. Since you still control the domain, I would suggest contacting the current hosting provider with proof of domain ownership and asking whether they can identify the account holder or help with the recovery process.
You can also check whether any backups are available through your previous developer or hosting company. If you manage to recover the website files and database, you may be able to restore the site on another hosting account. We had to look into a similar hosting access concern while managing the SAS Accountant website, so I understand how difficult it can be when the original developer is no longer available. Before making any DNS changes, make sure you have checked the existing email records to avoid disrupting your business emails.
It sounds like the critical error may actually be the second problem you need to solve.
The first priority is identifying the hosting provider (HostGator looks like?) and recovering legitimate access to the hosting account. Since the previous vendor did not hand over the credentials, I would avoid making DNS changes or attempting to rebuild anything until you know what access can be recovered.
Once you have hosting access, make a complete backup of the website files and database before changing anything.
Then check the PHP/error logs. The actual fatal error should be recorded there and will usually identify the plugin, theme, PHP file, or other component causing WordPress to fail.
If you cannot recover the existing hosting account, but your organization controls the domain and DNS, you still have options. You can establish new hosting and rebuild or restore the site there. I would keep the existing DNS pointed at the current server until you’ve determined whether the existing WordPress files and database can be recovered.
Since the server itself is displaying a webmaster contact address, contacting that address and providing proof that your organization owns the domain/company seems like a reasonable next step. They may be able to identify the hosting provider or account holder, although they should not provide credentials without proper verification.
I would treat this as a hosting/account recovery issue first and a WordPress repair issue second.
