Hi, sorry for the delay, I had just read your post and I could said "me too"
But I solved the problem and it works for two years now.
I explain my solution here, if the French don't afraid you.
I resume, a 7.5volts power supply, a passive injector, and a spécial home-made cable to bypass the RJ45 socket. The 7.5 v go to Vin-Gnd of the Nano to produce 5v wich is returned to the W5100. QED.