That could have shorted two of the wires and fried the NIC. How did it get sliced?
You might try a new NIC, they are cheap. A PCI NIC is usually less than ten bucks. Or maybe reinstall the drivers for the NIC.
The problem could also be the modem/router's circuits. Can you plug another PC into it and see if it works?
Lastly, are you SURE the new Ethernet cable is good?
I came home one day and went on my desktop to work (on leveling lock-picking in Skyrim) and when I turned on my computer it failed to detect my ethernet cable, I unplugged it and it had been sliced so I replaced it with a brand new one... that one wasnt detected either, I have looked at several other forumss and talked to my friends who work on computers and every single time I get the same message: "A network Cable Is Unplugged", but I look to my right and sure enough it sitting there plugged in on both sides, one in the computer, one in the router/modem (never figured out which one is which). I have my schools version of finals due VERY soon so if someone could help me it would be very appreciated.