WHAT NO

OR

Well let me be the first.
The statement you made about grounding the jumper on the battery post and not on the chassis is a major clue to me that you have a poor connection on the negative cable. Check that first as well as what CDOWNS said.
It seems to me that even with a weak battery the solenoid should still click. I think you may have a bad solenoid or a poor connection on the S terminal at the solenoid. Either of the above posts may well be your problem though.
If you can, measure the voltage at the S terminal on the solenoid while a
helper turns the key to start. Observe all safety precautions!!!!
If you get 12 volts then try jumping the solenoid S terminal to the large battery terminal on the back of the solenoid. If it starts, this will eliminate all the major players in the circuit , Battery, starter, and cable connections.