IF it is a G4 Mini...you could try booting into Open Firmware: on power button push, hold down "option+command+O+F". If it works, you should see a white screen with small black text.
At the prompt, type...
1. reset-nvram (press Return)
then type...
2. set-defaults (press Return),and
then type...
3. reset-all (press Return)
Your Mini should then restart. Maybe this will help. Good luck.
Also, might swap RAM out with known good memory. Reseating bad RAM = bad RAM. ( Can run Mini without the top in place for troubleshooting...just be careful.)