Mighty 1284p SPI / Ethernet how to get it work ?

Power should be fine; I had the same circuitry for a 328P-based setup where the same ethernet (wiz820io) module was working fine.

When using a static IP, the atmega does not freeze and I can ping the device from my local PC. The hanging only occurs when calling ethernet.begin() to fetch an IP address from the local DHCP server.

I'm on Arduino 1.0.1 btw.