Multiple drains blocked???

Hello All. I have used the site in the past with success everytime. My initial question will be as specific as I can be. IF anyone has questions or suggestions. I will add more detail including photos if they are helpful(made all the difference last time!)


About a year ago- I replaced the most upstairs bathroom sink.
the new sink has only a drain(no little hole for overflow)
Its a one piece molded sink.
Anyway- within the past week it has backed up completely.
I disassembled the trap and its clear.

I quickly snaked the drain/waste line and nothing. No improvement.

NOW!
-
I have a multi-level split level with the washer in the basement. The washer dumps into the slop sink. I do have a strainer/stocking on the washer outlet that I change frequently.

This hasnt been an issue in the past. but yesterday that backed up and flooded the basement a bit.
The water goes down but ever so slowly .

So I have a little plug next to the slop sink and snaked it.
and nothing.

So the slop sink does drain, but slow and the upstairs not at all.
The upstairs shower next to the sink drains fine.
No other sinks back up at all.
FYI - we do have a disposal in the kitchen in case that helps.
I prefer NOT to use them as I know they could add to the potential for back ups....

Should I just retry the snaking of the slop sink drain???

Any other suggestions?
The upstairs sink still does not drain whatsoever.

Upstairs toilet next to the no draining sink is also a bit slow.
If there are deposits, sometimes takes 2 flushes.

Time to investigate vtr piping.

drains

1. The slow sink upstairs has NOTHING to do with the overflow downstairs. IT could be a stopped drain, or just the common problem with sinks without an overflow opening.
2. NOT using the disposer can be the worst thing you can do. It MUST be operated periodically, even with just water, or it can corrode to the point where it will NOT run, nor will it drain.
3. The upstairs toilet problem is in the toilet itself, possibly an adustment of the water when it flushes.