I didn't have much luck, though the non-draining toilet now is a slow-draining toilet, so I got a little function but fear I may have made the source of the problem more difficult.
In my vain attempts to do it myself I thought I'd remove the toilet tank for possible better access to the clog than snaking through the bowl. No dice. And for my efforts I now have a leak from one of the bolts that anchors the tank. Nice.
So, in the morning the professionals get called in to fix things, including those I broke.
At least I have a job interview on Friday.