Hi Peter,
You can test to see if it is the connections or a starter problem.
Connect a voltmeter to the large terminal on the starter. There is a
threaded terminal post there where the battery cable connects to the
solenoid. Connect the positive lead from your meter to this terminal (not
the battery cable) on the solenoid. Connect the negative lead of your
meter to chassis ground such as the engine block or starter housing. You
should measure 12-14 volts. Watch your meter and have someone else turn
the key to start. When you just here the click and no starting see whether
the voltage remains up around 12 volts or drops low or to nothing. If the
voltage stays up, you have a starter problem such as worn out solenoid
contacts or brushes. If the voltage drops way low when the key is turned
to start, you have a connection problem such as corroded /dirty battery
terminals, corroded or loose connection between the positive battery cable
and the starter solenoid, corroded or loose connection between the negative
battery cable and the engine block. All of this assumes you have a good
battery, of course. Hope it helps,
Mike