OK, thanks for the update. You said ‘if I touch this joint with a pick, it starts connecting.’ That’s a strong indication of some soldering related issue, or perhaps the chips are not inserted in properly.
One thing I suggest you do is to turn the unit on and measure the voltage from each pin of ENC28J60 to ground. I know this is a tedious test, but it’s the only thing I can think of that would provide more information about what’s going on. There are 28 pins on the chip, start from the top-left pin, goes down, then move to the lower right pin and goes up. That way you get 28 voltage readings. If you can post these readings here, I can compare it with reference and see if there is anything obvious I can tell.