In addition to Leon's suggestion ... question ... did you transfer the backups to the new hosting environment via FTP? Was the FTP transfer done in binary mode or ascii (text)?
Migration consist of code + DB + minimal moodledata/filedir/
If you transferred correctly (binary) and did all of moodledata, the cached directories in moodledata still refer to old site ... suggest manually removing *the contents* of moodledata/cache/ and moodledata/localcache/ directories ... that's *contents of* and in moodledata (not code).
Also, if server moved to a different provider, that would mean a change to DNS. A dig (DNS lookup) for your domain shows the IP is: 22.214.171.124 which belongs to Bluehost. Is that the old host or the new host?
DNS changes could take a couple of hours or a day ... depending.
Right now, going to site via browser, site appears to be in limbo ... gets redirected to a cgi/suspendedpage.cgi and on that page recommends contacting the webmaster.
Please see, if you were not aware of that: