Hey Torkijo,
How much have you tried? when I had the problem I went through the routine of checking all the connections (some of the WIKI has somehow lodged itself in my head, whew - though an iphone would have helped too!). Naturally disconnect the battery to avoid zapping ones self - safety first.
Note (on a diesel) the nearside starter motor bolt that goes through the clutch slave cylinder bracket also acts as an earth, so clean up there too. I know this because on another occasion I mistakenly didn't have the right tool for the job (sacrilidge

) and couldn't get it done up tight enough with an adjustable, it eventually worked it's way loose and she didn't start no more, well did sometimes with a whack of a hammer (in effect an earthing effect) so I thought it was on it's way out but had it tested at local sparkys and said it was fine, lots of headscratching on that one.
So when I had done the earths, checked fuses etc, I figured screw it - take the starter off for a close up & because it was easier to get the sandpaper on it rather than lying on my back (due to gravity the bits of sand fall in your eyes

) That was when the bit I tried to undo - the main power to the starter (the really thick wire on the big bolt that is normally also attached to the battery on the other end of it) which is on the solenoid - that's the bit that sheared off, the bolt & nut was stuck to the eyelet on the wire - corrosion. It seems the plastic end on the solenoid had cracked through vibration over time and had caused enough of a gap inside between the connections for the starter not to fire when required.
The copper pipe trick and tie-cords was purely a temporary fix to get me out of the pooh. I 'borrowed' another starter from my project bus is the honest answer of how to 'fix'

however from the second pic in the post, you can see that there are signs of a pending failure through cracks on that one too! (vibes - so people, make sure your fat +ve wire is suitably supported with tie-cords or it'll go eventually - usually up a mountain or somewhere equally handy)
people suggested that I find the part number on it and see if I can get a replacement solenoid. Will get round to taking it to a local sparky soon...
I seem to recall a new starter costing me about £100 a few years ago, not sure if I had to hand in the duff one as exchange too
Hope that helps,
Brent