Technical problems with hosting/domains/coding on old wordpress themes for 2 sites

I have 2 client websites that have been developed on very old wordpress themes. I have had to have them migrated onto a new servers and since their transfer, they are not showing.

There are issues with domain pointing as well, but I do not have technical understanding to resolve. My hosting provider says there also may be issues with coding.

I need someone to just look into the issues and clarify exactly what the issue is and recommend steps forward. I would prefer that this person also has the ability to talk to hosting provider to help with resolution