The solenoid is basically a huge relay to supply current to the starter. On an inertia starter mini it's attached to the drivers side (O/S) inner wing just behind the fresh air duct. It's a square box with three terminals (2 big one small). Big ones are +12v from battery and +12v to starter and small one is the supply from your ignition switch to engage the solenoid.
A good way to eliminate earthing / wiring problems in the starting system is to use jump leads to (temporarily) bridge each connection. Once the problem disappears you know which connection is giving you grief or whether you have a faulty starter / solenoid.
For example, to check the engine block earth: Connect a jump lead to a bare metal point on the engine / gbox and connect the other end to a bare metal point on the body. Do this with every connection in the starting system while attempting to start the car each time a new connection is bridged. If the starter suddenly comes back to life you've found your problem. If not you've isolated a starter or solenoid fault.
Connections to check are as follows:
1) Battery positive to Solenoid [+12v]
2) Solenoid to starter motor [+12v]
3) Starter motor to engine block [Ground]
4) Engine Block to Car Body [Ground]
5) Battery negative to car body [Ground]
Note: connection (1) is difficult to test with jump leads as it runs all the way down the car (too long). I would check all the others first then if no results, try connecting jump leads from another car battery directly to the solenoid + and engine block. If the starter comes to life you've found the problem.
Note 2: Be VERY careful when doing tests (1) and (2) not to touch the leads to any ground points (engine/gbox/body) whilst connected to +12v... this will result in sparks.
If the car still will not start whilst doing this test, the problem is with either the starter, solenoid or battery. Sounds like you've eliminated the battery by jumping so next step afterwards would be to check the resistance of the solenoid.
I've used this method to track down a starting fault on a friends fiat punto and it worked a charm... we tracked the fault down to a faulty starter, replaced the starter and bingo... no more sluggish cranking.
