Well, probably starter, but worth checking the following basics:
1) Main battery conections at battery(ies), and battery voltage (if no meter, just turn on headlights before cranking: if they go very dim when trying to crank, suspect failing battery).
2) Main earths at battery(ies).
3) Main power lead into starter (or solenoid if running seperate one).
4) If running seperate solenoid, then lead from this to starter.
5) Engine earth lead: easy way of checking is to put jump lead between car body (earth) and engine casing (engine earth). If cranking improves suspect engine earthing. OR: if you've got a multi-meter, set it to volts and hold one lead on a good body earth (like one of the engine bay earths), the other lead on the engine casing. Get someone to crank the engine: if you get more than .25 of a volt (give or take) you need to sort your engine earthing. (I always run two, as they are so cheap, and can cause all sorts of mischief if not perfect).
You can take it that your ignition lock, ignition wiring and the lightwieght solenoid leads are all O.K. as the solenoid is clicking in and out.
Your problem is almost certainly poor contacts within the solenoid: three options, assuming you've got a combined starter/solenoid (most common):
a) Replace starter.
b) Fit second solenoid, move main battery lead to this, add 2nd lead from solenoid output to starter main terminal, and move solenoid activating lead ( the lightwieght one) to new solenoid, thus bypassing original unit. Really a bodge to get you back on the road if you can't find the right starter.
c) Sometimes you can unpick the crimping on a solenoid, get to the contacts and just clean them up: usually it's only years of arcing that makes them intermittent.
Like I say though, it probably will just be a case of putting an exchange starter on, the rest is for general info really
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