This might be tough to track down. From your description/system behavior this could be any number of things. Faulty component or hardware, defective MB, electrical fault. The system is failing during POST, pre-boot environment when the system is performing hardware verification before hand off to the OS loader.
Ensure your PSU is not failing, I'd test with a second one if possible
Then...
Test your memory with windows memory diagnostic or memtest86
Test boot with each stick of ram individually and in different slots
Remove processor and inspect socket for bent pins
Remove and reseat, memory, add-on cards, CPU
Inspect the MB mounts and ensure nothing in the case is grounding
Reset CMOS
Pull battery and disconnect from power (wait about 5 min) reseat and reconnect to power
Replace the MB battery
Inspect capacitors for bulges
If you want to go further, you can remove the MB from the case and inspect with magnifying glass
Do you still get error code 66 if you disconnect the boot drive and attempt to start the system. This will confirm pre-boot error.
If you were only experiencing the NIC and shut down hang, I would be inclined to say the problem was related to software, but the code66 would indicate hardware instead. Good luck.