Having a look at the switch matrix, all your symptoms are explained by the DIN input for that row always being “grounded”… look at the list of switches on that row: Osc Sync/Ring, Mod Osc 1 PW, Mod Src 4, Menu, Down, Select 4, SID 1, Play… i.e. regardless of the currently selected “column” of the matrix, the DIN input is always low and therefore the app thinks all those buttons are pressed.
The flashing cross is what you would get if you pressed Mod Src 4 with Mod Osc 1 PW… the corresponding row and column will flash while you make the selection and then stop after you release the buttons. The display would also jump to the Modulation M4 screen. The stuck Middle C tone is because the Play button considered pressed.
It might be the LCD shorting it, try unmounting it.
However, my prediction is a short between/near the 74HC165 pins.
See attached pic. That’s where I think there’s a short, since that’s where ground and that pin/track are closest.