The driver, probably, but it would need to be looked at either by JBL or a local reconer to know if there has been other damage.
The white rectangular bit is just a cheap wirewound resistor, probably 10W or so but it should be printed on it. Go to RatShack or the like and get another to replace it and solder it in. Maybe $3 and 5 mins.
Resistance and wattage will be printed on it.
the one time i had to deal with JBL it was a piece of cake and the person on the phone was really nice and helpful. But all i was doing was ordering a new speaker grill. If you cant find contact info let me know and ill look it up in my manual.