Dog chewed on power cord, laptop shut off while plugged in...

I unplugged the power cord from the MBP and the wall, turned the laptop back on, battery icon at the top shows an X through it. Looked at some solutions at the Apple support site and one said to connect the power cord but I don't think that's a good idea. Did the chewing on the power cord damage the battery? The laptop is still running off the battery because I'm typing this from it but I am unable to see how much power is left. I guess I'm going to get a new power cord and adapter and see if that fixes it? What do you suggest?