Just to stir the pot slightly, here is a link to the PC specs:
As usual, the LAN port is built into the motherboard. The expansion slots are as follows:
1 PCI Express x16 (Gen 2.0)
3 PCI Express x1 (Gen 2.0)
1 PCI Express Mini Card (Gen 2.0)
There is only one PCIE x16 slot which will be used up by the video card. So, if the LAN port on the motherboard is fried, you will either have to replace the motherboard or install a PCIE x1 LAN card.
The interesting news is that the built in wifi is a Ralink RT5390 802.11b/g/n WiFi mini-card, which can actually be upgraded to a card which can run both 2.4 and 5 Ghz wireless networks. So, if you ever desired to run the pc via wifi only, you should consider upgrading the card so that you can get out of the 2.4 Ghz crowd.
So, my first bet would be to swap the modem and go from there. In the event that something is fried within the modem, you won't be sure about the LAN port on the PC until the modem is swapped.
One other point is to consider the surge protectors. There are surge protectors, and then there are surge protectors. You have to review the Clamping voltage, Energy absorption/dissipation, and Response time of the protector. When you compare one against the other, you will see that there is a wide range of protection available across many products. I think that people generally make an assumption that, "Ok, I've got a surge protector, I should be safe from lightning strikes or power line surges." Unfortunately, with such a wide range of protection capability available, from very little to very good protection, that assumption may be overrated. Not saying that is the case here, just pointing out the considerations of buying and installing a surge protector. Personal opinion, if you are going down that path, consider that the surge protection will not protect you from a power outage, which if it happens, could cause a disk crash. That is a considerably more painful event to recover from. So, consider going to an uninterruptible power supply, which usually has plugs which will run off the battery and some which have surge protection only. It doesn't have to be huge, just enough to run the pc and monitor so that you can shut down the pc in the event of a power outage or nearby lightning strike.
Here is are a couple of links that offer brief explanations:
http://electronics.howstuffworks.com/everyday-tech/surge-protector7.htm
http://thewirecutter.com/reviews/best-surge-protector/