This is hard to say on the information provided. Firstly I would be very surprised if lightening has just knocked out the ethernet port and left the rest of the PC alone..(presuming you dont mean the phone jack to the modem)..
If the ethernet network interface to the PC has been damaged and the rest of the PC is ok you may still connect to the PC by installing a PCI network card or using a USB/ethernet interface..
Im not sure what you mean by "running a new wire" Maybe I have not understood the situation fully..