Basement floor drain back up, 1/2" snake failed, what next?

I had to deal with a similar problem recently, floor flooding when washer was draining, and what worked made a huge mess but it worked: I filled the vent stack with water (going up on the roof with a hose. It flooded the sink, but all that weight it pushed through eventually.)

If you try this, try and plug the drains on the first floor, and the laundry sink. Otherwise as the column of water in the vent builds up it will be flooding out of all your drains. Once it bursts through you'll heard it whoosh out, and all your drains should be flowing. This will not work as well if your toilets are on the same vent stack. In my situation the kitchen (on first) and the laundry (in basement) were sharing a common vent.

Using a shop vac try sucking on the washer drain line. First fill up the washer drain line with water, then quickly putting the vac hose over the drain.

If you know which is the first sink or toilet below the location of the blockage you could run water into that drain and then put the shop vac on the washer drain. The idea is to relieve the blockage by forcing water in the opposite direction. Sometimes this relieves a blockage when forcing water in the normal drain direction only packs it tighter.