I see - the applet is signed; you didn't mention that before. But the applet tag still doesn't point to the DB driver jar file (which also needs to be signed).
Note that using JDBC in an applet is generally considered a security risk. You should consider using a proxy on the web server instead that the applet would access via HTTP, and which in turn uses JDBC to access the DB. That also obviates the need to open up the firewall on the Mysql port.
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