so what character set were you using on your old server?
what character set were you using on your New server?
consider settign the default character set in the new server to be the same as the old server, if you cannot do that then consider changing the character set for each table on the new server to match the old server.
you may need to do a dump of the data,
dump the schema,
then edit the schema and reload it
the reolad the data
suitable tools may include MySQL Administrator, PHPMyAdmin......