P bass buzzes with preamp under strange conditions

Hi,
I have a strange problem with buzz. When I plug my player p bass into Ampeg scr-di preamp it buzzes. If i roll the tone knob completely off, the buzz stops. I took pickguard and bridge off to see, whether soldering was ok, and it was. I also took tone and volume knob caps off. After putting everything back the buzz thing changed. Sometimes it creates another (yet similar) additional type of buzz that blends with the old one, if the volume knob isn’t all the way up.
I tried the pbass with VOX headphone amplug headphone amp and there was NO BUZZ generated by the bass (only white noise that was produced by the amp), regardless of anything I did with the knobs. This headphone amp is powered by batteries. Also tried plugging p bass into my combo amp and it produced only a small amount of buzz when rolling the tone on (the amp has a lot of buzz itself, but the SCR-DI is absolutely silent when cable isn’t plugged in). Then, confused AF, I put my other bass (Ibanez with onboard preamp) into the SCR-DI and it DIDN’T BUZZ at all. I tried plugging the SCR-DI into different socket with the same result.
Please, do you have any ideas, how to get rid of this terrible buzz?

 

I also checked grounding with a multimeter, and everything was fine.

 

Yes, it did show continuity. Its not a real multimeter, just a LED and some cable.

 

Thank you for your effort, but cable was the same.

 

I checked it multiple times, but it still looks like connectivity is all right.

 

Yup.

 

Yup