Ahhh...it is possible that the MySQL installation you are trying to import into doesn't support MyISAM. That's a possible but seldom used option when installing MySQL.
SO that would explain the inability to import MyISAM, at all.
Doesn't explain why changing from
ENGINE=INNODB didn't work, unless you have data integrity problems the MyISAM ignored (as it almost always does) where INNODB choked on them.
For that, I'd need the complete error message to hope to diagnose the problem.
Perhaps a better approach would be to create a temp database on the *OLD* system and create the tables in that temp DB as INNODB. Then use SQL to copy the data from the MyISAM tables to the temp DB's INNODB tables.
If that works, then dump the temp DB tables and import them.
An optimist sees the glass as half full.
A pessimist sees the glass as half empty.
A realist drinks it no matter how much there is.