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Wow, what?
Between the trimpot and the PSU's GND there is a voltage of 0.018V
Between the trimpot and the USB's shell there is no voltage
Between the trimpot and the DRV's GND there is no voltage
But, USB's shell and the GND of PSU are connected, as well as the USB's shell and DRV's GND is connected. Also all GNDs of DRV's are connected.

I wonder how is that even possible? And I have an answer, it is not (as I was taught...). Well, I tried to measure it again, and again, but I get the same result every time.
So I assume the only faulty thing here must be my multimeter? Indeed, I don't think so - the multimeter is fairly new and disappoints me only when measuring resistance. It has always given me good values of voltage.

Other measurements:
Between fault and GND - 0.4V (logic power supply) - it should be 2.5-5.2V..
Both GNDs on the DRV are connected.
Reset (I couldn't identify sleep pin) is not connected to Vdd.

B1, B2; A1, A2 - B with B and A with A show the same resistance (although, it is about 1710ohm? well, maybe my multimeter is wrong). What's interesting is, that when I connect the motor, this resistance drops to +-1660. Like, what? BTW, when I turn on the PSU, I can't measure any resistance here (even with motors connected).
Motor coil resistance is +-46ohm for both.

I guess RAMPS and DRVs are ignoring all the laws of physics :D

Told myself to do some more measuring:
Voltage between all trimpots and PSU's GND is 0.018V as I wrote before. With the exception of Extruders DRV - 0.01V here while trimpots are turned the same on every driver. You might think that it is because I only tested XYZ motors and drivers and E is the only working now, but nah, the E motor was running as well.
So I measured the resistance on D10 - Extruder's heater - to test my multimeter. It's 4Ohm (+-); 1212/4 (UU/R=P) is 36W, so the multimeter seems to be all right...

I'm feeling kinda hopeless now :D I have to go to sleep now, but tomorrow I will probably measure same things on my geeetech printer (although, I believe I have A4988 there :/ ), hopefully something will ring a bell.

I (we) have to figure something out, I don't want this to be wasting your time.

PS: Should I replace the DRVs with A4988 from my geeetech or vice versa? Seems like good idea to me.