Welcome to LisaList Alex,
Others may have other suggestions, but here are my thoughts:
In general, if you have had battery corrosion and the Lisa won't power up when you push the button, there may be a bad trace on the I/O board (these two things often go together). Double check that area and test the continuity of the traces and vias as well as making a visual inspection.
More specifically:
If you've found the power switch signal is reaching the COP421 at pin 20, but it isn't turning on the power: check the COP has power (pin 9 should be approx. 5V), and check it is not held reset (pin 4 not below 2.5V), and that pin 1 is truly connected to ground.
If you have a moderately high impedance probe, check the COP oscillator is running (approx. 3.9 MHz at pins 2,3). If not, check the parts/circuit connected to pins 2 & 3.
If it all looks good, and the COP oscillator isn't running or pin 24 still refuses to switch, then the COP might be bad, but triple-check it is making good contact in the socket.
Note that the COP will only turn on the power... if the power is already on, the power switch won't turn off the power unless the 68K CPU is running and executing some software that is watching for the power switch.
After getting the COP turning on the power, I'd start working on the CPU problem... horizontal bands on the screen is typical when the Lisa is not running well enough to start the memory test. I may seem like a broken record/skipping CD, but I'd first check/clean the card-edge connectors for the CPU, I/O, and memory boards.
Good luck!
James
... it won't start. The motherboard was badly corroded but I cleaned the corrosion
...
... on the COP421 chip I can measure the power button signal when I press the power button but the state of pin 24 remains the same
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