I believe for this model corolla, if the radio has the security feature the screen will say "SEC" until the proper code is typed in.
Make sure you check all the radio fuses with a volt meter or test light. Specificaly, check the dome light fuse and cigarette lighter fuse as those power the radio.
Here is the radio wiring diagram for a 2004 Toyota Corolla:
2004-Toyota-Corolla-Radio.PDF
You can use those wire colors or pin numbers to make sure you have power at the appropriate pins in the radio harness connector.
Good Luck.