I bought the cheapest lawnmower in Ireland! how bad is it???  

Well it turned out the solenoid was working so it was the original solenoid I put back in. The issue was the 12 volts wire from the key wasn't sending enough voltage to engage the solenoid so I replaced that and reinstalled the solenoid. The earth for the solenoid is the frame of the machine just like the starter and most other electrical equipment on any machine so if your having a bad connection take it off and wire brush the back of the unit and clean the plate where it is bolted to and that should give you a good earth. If that doesn't work look at the main earth on the battery connector and where it bolts to the frame of the machine if that's rusty or dirty your connection won't be strong enough for smaller power needing unit's especially like LED lights. Hope this answered your question have a good one 👍