Does your Corolla burn oil (wet oily mess in the tailpipe is a bad sign)? That can plug up or coat the cat substrate. Assuming you have no intake or exhaust leaks (especially intake manifold gasket) and your O2 sensors are new DENSO brand sensors, you can remove the section of the exhaust with the cat converter (it's not hard to do). You should be able to view into the exhaust right before the cat and see if the "honeycomb mesh" substrate is plugged up. If you have a video boroscope (you can get them cheap now), you can feed that into the O2 sensor bung opening and take a view of the back side of the cat substrate also. If you have no intake/exhaust leaks, and properly functioning O2 sensors, and the cat isn't plugged up, then your cat is probably no longer efficient enough. There are cheap replacements you can get ($130 on Amazon) but I have no idea of the quality. After about 350K miles or so, my cat gave up the ghost. A rear O2 sensor replacement at around 250K got rid of the P0420 for a while. So, around 350K I used a spacer at the O2 sensor bung opening and the P0420 went bye bye. My cat substrate was very clean, btw (don't know if it was previously gunked up, because I ran lacquer thinner before removing it).
Make sure your PCV is in good working order and that you don't have a leaking valve cover gasket.
Lastly, some of the 2004 (and 2003 or 2005.....can't remember anymore) had a TSB issued stating that a PCM/ECU updated calibration was available to give more flexibility to the cat efficiency threshold to help solve the P0420. It costs one hour of labor from your local Toyota dealer to do that recalibration (the TSB says it takes 8/10 of an hour, but the dealer is gonna charge you the whole hour). At least that's what they did to me even with me pointing out it was 8/10 of an hour on the TSB. I think I paid $107 several years ago. Make sure they give you a sticker which shows the recalibration was performed. You put the sticker on the car somewhere (underside of hood or perhaps in the door jamb).
Here's the link to the $130 cat exhaust assembly on Amazon. It shows "
currently in stock". 83% 5-star reviews, 13% 4-star reviews, 5% 3-star reviews. Zero 2-star and 1-star reviews.
Buy TED Direct-Fit Catalytic Converter Fits: 2003-2008 Toyota Corolla/Pontiac Vibe/Toyota Matrix 1.8L FWD 1ZZFE: Catalytic Converters - Amazon.com ✓ FREE DELIVERY possible on eligible purchases
www.amazon.com
Here's an example of an O2 sensor spacer (only use this if your cat isn't plugged up):
Buy Stainless Steel O2 Oxygen Sensor Spacer Expender M18 x 1.5 Thread 45mm (1.78") Length SS 304: Automotive - Amazon.com ✓ FREE DELIVERY possible on eligible purchases
www.amazon.com