Do some "voltage drop tests" across all the battery & alternator
connection... this will tell you if there is a bad connection
(too much resistance) in one of the cables.
Voltage Drop Testing procedure:
http://www.aa1car.com/library/voltage_drop_testing.htm
or
http://www.vernco.com/sparks/id606.htm
What happens when you manually activate the starter under
the hood? Find the starter and apply battery power from
the "+" terminal to the solenoid "trigger pin" on the
starter (#3 on this picture).
http://faculty.ccp.edu/faculty/dreed/Campingart/jettatech/nocrankdiag/starterprea.jpg
If the starter turns every time you use a wire to activate
the solenoid, then you have a problem in the power supply
circuit to the solenoid.
If the starter does not turn like this or just clicks, then
you have a starter problem.