You could write a PHP script to read in the csv file (fopen), then make a SQL insert for each row. Echo everything out to the page first, and check to see what the line breaks are like and see if you can use nl2br to convert them, then put it into your database (one row at a time) and see what happens.
If you echo out your sql insert statement first, you can copy/paste it into a MySQL frontend tool and see if it executes