[IHatePlumbing]

The water will not drain from our kitchen sink and a toilet. However, the two bathroom sinks, two showers and other toilet drain perfectly fine. We have tried Drano, a power "snake" auger, a toilet auger and a plunging with no results.

We do have a septic tank, but my guess is if that was failing, none of the plumbing would be draining/working correctly.

What does it mean when two things out of seven are not draining?

Thanks!
Now You Know Why I Hate Plumbing

[speedball1]

Sounds like you may have two problems. If you've augered the toilet then the blockage must be in the toilet drain line. For that the toilet must come up and the line snaked. But first go back and auger it again.
Tell me what you did to the kitchen drain. Did you snake from the trap? Let me know. Tom

[KISS]

Another possibility is the vent, the pipe that goes to the roof. What's the proximity to the vents of the 2 items that won't drain?

You need to look at drain and vent routing.