On the purple A600, it sounds like the green RGB component is not working.
Sometimes this can be caused by a coil in the delay line Z222 going open circuit.
The SD/FF probably requires power from the RGB port, check that you have +5V on pin 23 and +12V on pin 22.
Check the RGB output using a C= 1942 or similar monitor.
Using an oscilloscope, check you have RGB signals on input pins 2, 3 and 4 of the video encoder U12, and you have RGB output on pins 21, 22, 23.
It's also possible U12 is faulty.
A600 schematics here if you need them:
http://amiga.serveftp.netAs for the green LED flashing A600, it sounds like it's constantly resetting.
Probably a bit harder to find. Could be anything from memory access problems, CPU problems, ROM problems, etc.