Try out the standalone memory test from EXOS 2.4 beta! (twp8ukc.rom)
It is a big bug in the original EXOS test, it is use a CALL instructions to test the system segment. But if the onboard memory is bad then the return address corrupted, the system is frozen, no picture, no sound, no life sign... only see a random picture, because the Nick is running uninitialized and using the poweron random filled bytes from the video memory.
In this test version included my "BEEP test" routine, it is start testing the system segment, writing 00h,FFh,55h,AAh to each bytes and reading back, and say with beeping sounds the readed bits, low sound for 0 high sound for 1.
With this method you get confirmed the machine is least partialy working. And if you detected which bit is bad then know which memory IC is needed to replaced.
This test not use CALL instructions, only run in the ROM.
The BEEP test is started immediately if you put the EPROM to the motherboard ROM socket, using as test EPROM.
If you use on the normal place (the full EXOS 2.4 or the standalone version in the cartridge at the 04h segment), the BEEP test can be forced by pressing down the B key at power up.
And normaly before testing start the system segment (using CALL instructions), test the first byte with all 00-FFh values, if error detected then the BEEP test started.
One additional experience: I found few defective Z80 cpus in dead EPs which is cannot write memory correctly.