This is going to be long.
First check house policy see if you have blocked drain cover.
Open the manhole the stack pipe feeds in to see if it's full if yes and their is another manhole check that if that one is empty then it's between manholes. Rod using the rubber plunger attachment but Duck tape the rods on the joints and ONLY turn CLOCKWISE because they can come un-done and so will you if you lose rods up the pipework.
If the manholes are clear it will obviously be in the stack pipe maybe a chunk of the old toilet pan dropped in the pipe if they had to break the old one out. Was anything coming out the washing machine stack pipe collar when you removed the washing machine pipe?.
Carefully and stand back a bit if you can, remove the blank then if nothing comes out and it is looking clear [torch light] then I would say something HAS been droped in at toilet end by accident. Messy if it clears but leave blank off and use the rod plunger or sink plunger in toilet see if that clears it. Some times a very strong caustic soda mix in VERY hot water poured into the toilet pan clears a, soft material blockage, which hopefully this is. Give it a go but use rubber gloves as caustic soda itself burns if it gets on wet hands and is painful.
BB
December 2009