Sorry for the double post - nobody seems to have any ideas, so I went back to play with it again with some new tests of my own. I think I made i worse 
I wondered if the noise could be coming from the power supply (the supply I’ve got seems to put out the right voltages and stuff, but the plug feels ever so slightly “loose” in the socket), so I tried powering the Shruti with a 9V battery instead. The Shruti powers on fine with the battery, but the electrical noise is still there.
It was at this point I discovered that I seem to have killed the LCD screen somehow. The light comes on when the Shruti powers on, but I no longer see anything on the display. Any ideas what I might have done, and how I can test and rectify (or replace!) it?
The buttons, knobs and LEDs still work despite the dead screen, and I can still play the test tone, and notes from the keyboard, and edit the sound - just nothing on the screen. Another thing I noticed that I hadn’t before is that when any of the buttons are pressed down, the sound of the electrical noise changes - becomes more “buzzy” - and then changes back when the button is released. Any idea what that could be?
To rule out any problems with the interface board, I removed it, and tried just powering on the main board whilst it’s connected to the amp. Can’t play a test tone because there are no buttons plugged in (I didn’t have the keyboard plugged in at the time, but I presume it would have played notes) but I was only really listening for noise anyway. Still there. So there’s a problem with the main board (or with the switch or pots).
I took a look at the main board under a good light and a magnifying glass. My soldering isn’t the greatest in the world, but I couldn’t see any obviously dry joints - can you see anything in the following picture?
(Oh, the shame…)
Grounding the pots hasn’t helped, but they still seem like they might be the likeliest suspects. Is there a way I can short them, to get an idea what the Shruti would sound like without them, or would I have to physically remove them?
Any help with any of these questions would be great. Right now I seem to be breaking the poor thing more every time I go back to try to diagnose why it’s so sick in the first place 