Disconnect everything except the Chip RAM SIMM and the power and display. Then turn it on. You should see the screen turn black, and then a momentary sync on the TV while it resets the AGA chipset. The screen will eventually turn purple (hopefully). If it doesn't - wait some more. Wait a few minutes. Perhaps an hour. There's reset circuitry that waits for a stable voltage, and this can take a long time if the caps are bad.
Next: Turn it off and put the keyboard in. Start up the Miggy, and when it's been on for a while, press the CAPS lock key. It should light. Press it again, it should extinguish. Then press it repeatedly many times. If it stops lighting/extinguishing, then the CPU is not doing anything. If it keeps doing it, the CPU is working.
If you get any colour on the screen other than black, tell us what it is.
I had this problem with my beloved A4000 - the screen just stayed black.
After recapping it entirely, and rewiring the power supply, I eventually tracked the problem down to something more simple - it was just the Alice chip that had come a little loose from its solder points. 30 seconds with the Aoyue rework station, and it's worked 100% ever since.