I have the exact same symtoms. I did not have any of the parts replaced though. I have fought with error42 and 44 before. Those turn out to be an A-coil that is too small to let the proper air flow through. I had to remove the end cover of the a-coil to let air pass around it during this winter.
As far as error 32 mine will also work after powering off the furnace for 30 minutes or longer.