No Heat in Our Van

Hello all! We have a 2002 Honda Odyssey Van. We recently had the timing belt changed. Soon after that, our heater quit working. We have had the system flushed 4 times and changed the thermostat. We have been to 2 different mechanics (one being the dealership) and they say the next step to try and fix it is to replace the heater core. This is a couple thousand dollars to fix and they don’t really know if this is the problem or not. Any other ideas what it might be? The air that does blow out is cold and it doesn’t really blow out much of that. Seems like there is a clog??