2000 Ford Contour Won't start

My daughters boyfriend drove his car here and parked it.
After about an hour he went to leave and the car wouldn't start he tried to jump it with my daughter car and nothing. It just clicks when you turn the ignition
The next day after looking at a old 2005 Wall-mart battery I assumed it was bad and replaced it. When I tried starting it the speedometer went to about 70 MPH and the wiper went to intermediate and then later the dome light would not shut off and it still would not start.
After talking with his mechanic he advised him to tap the starter while trying to start it. I don't think that will do it but to satisfy him I'll try it. Any suggestions.