either the nic on your mac is bad or your switch is bad. if the port that your printer is plugged into is working try plugging your mac into that port. If it still does not work and your sure your cable is good then your nic is faulty.
you will need to use the battery designed for use with your laptop. look on the battery and get the model # and order the same one. when you get your new battery be sure and run your laptop on battery and let it drain to about 10% after it fully charges. NEVER leave it plugged all the time.