Are you tried to change database table Collation ? Please try once
Login to phpmyadmin > select your database > Operations > now change Collation from drop-down to "utf8mb4_unicode_ci" or changes to other what was in your old server.
I hope it will work for you.
see screenshot: http://prntscr.com/8ip1ro/direct
Remember: If you export sql file from your old server to your pc and open it with any text editor... and customize and save.. then please check .. when you save the sql file.. Text Editor "Encoding" is Utf-8 .. see my screenshot: http://prntscr.com/8ip2nr/direct
Thanks