A Corolla service manual for free is a joke. Service manuals are Written by manufacturer companies, or authorized publishers like Haynes and Chilton, and cannot be shared for free on the Internet.
The copies that are published online are stolen and not authorized. Here is an example of free but not original or authorized download: toyota_corolla_-_2004_repair_manual.zip.
Using the link above, you can download a copy of service manual, but since copy is not original, I suggest buying the original paper hardback from Haynes for about $20 from link below.
I am a classic cars repairer, and I can ensure you that when you do a repair you need the book, you do not go back and forward from computer, and printed sheet are quite messy.
All I can give you for free is a complete wiring manual. This should be useful enough to fix stereo system, wiring and electrical problems.
To download the file, please, click here !
Regarding the complete service manual, for a small fee you can buy a copy here:Toyota Corolla Haynes Repair Manual for 2003 thru 2005
Below also an interesting website.
Toyota Corolla frequently asked questions (FAQ)
Please, do not forget the feedback.