The error message suggests that there is no ajax response due to a fatal error somewhere along the way. Turning on the error reporting in the wp-config.php might print something into the request.
As long as the wordpress paths are correct the search paths should be correct as well. You haven’t changed the domain, so everything should be ok.
Try to open op every settings page from the ajax search pro submenu and save them again. Maybe some of the options were lost along the way – I would say most likely the caching options.
Also deactivating/activating the plugin sometimes helps.
If nothing helps you can provide temporary ftp and amdin access and I can try to debug through the ajax handler to see where the error comes from.Best,
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