We have a lot of missing information such as:
- how were the files uploaded to the new Host
- when did you change Nameservers
- how was your previous SSL Cert installed / transferred to the new Hoster
- was PHP running as CGI on the old Server
You can solve the riddle of whether it's an SSL or PHP problem by changing the SSL setting in your two 'configure.php' files to false.
Also, why would you experience any downtime? You should have had a Dedicated IP address for your Hosting account with both Hosters, for use with your SSL Cert. With the new Hosting account you use your IP address within the Zen Cart 'configure.php' files to make sure everything is OK. When it is, you then put the old Hosting account into Maintenance Mode, change Nameservers, change the new 'configure.php' files from your IP address to your Domain name and you're away. Perhaps though, that is good information for next time?

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