I just replaced my speakers in my 2004 SE Corolla. I am not an expert on speakers and stereos but here is what I found. First off I had washed the car just before driving home and taking the door panels off. I found water inside the doors. I would be interested to know if you find the samething.
The tweeters in the doors are wired striaght to the 6.5 speakers. No crossover. The tweeters put out almost nothing. I replaced them with JBL 6.5 component speakers GT0606C. The JBL tweeter has much better sound. The JBL tweeter even fits behind the current tweeter cover.
I replaced the 6X9's with JBL GTO936 for the back. The 6X9's are ok but not as strong as I wanted. I hooked everything up with a Rockford 600 watt punch amp. It sounds pretty good for the little money I spent.