Pressing the power button a few times quickly is the same as plugging and unplugging the player, so there's nothing really new in that information.

Although, since that behavior of the power button is coded into the protected boot firmware, it is another indication that the problem doesn't lie in the firmware.

Have you checked to make sure it isn't something silly like a bent pin on the ethernet port? Have you dismantled the player and looked for broken solder joints around the ethernet port?