It sounds like the starter solenoid to me. You say that you have electrical power, and jumping it still won't turn the starter? Definitely a solenoid problem, unless......Is this car a POSITIVE ground car, and if so, I hope that you considered that when trying to jump it?
Do you have 12V at the solenoid when trying to start it?
On their death bed, nobody ever said, "Gee I wish I'd spent more time at work!"