does the LAN work ?

So I got anxious to fix it and removed the more problematic chip. The board still works but one lan port is dead. The other lan port works fine and the remaining chip is no longer getting hot. So I think mission accomplished.

Just to add some more in case someone else had this issue ... it looks like a couple of the pins burned up or had some corrosion. I am guessing this is what was causing the overheating or maybe this was the result of the chip shorting out. I used a cheap desoldering heat gun I bought on Amazon to remove the chip. I surrounded the areas with Kapton tape and put flux on the pins of the chip. I then heated slowly increasing temperatures. I had to go up to about 450 degrees but I think that is because it is a cheap air gun. I think starting around 350 - 400 should be enough. It takes a little while to get it to heat up so be patient and use tweasers to remove it as soon as the solder melts.

The board seems to be working fine now and I still have one LAN port working. Hopefully, none of the surrounding components were damaged ... mostly concerned about capacitors. I didn't run it long with it overheating but not sure if the prior owner did. I didn't try the LAN ports prior to the removal but my guess is it was working intermittently at best if they were using the board before the damage occurred ... who knows?