While you're in there, and apologies if all the following is blindingly obvious, but set your multi-tester to check resistance rather than voltage/continuity. It may reveal a high resistance circuit somewhere. If you get no joy, switch back to voltage, and, starting with the battery, the next check would be to see if the first part of the kill switch has voltage, then cross to the other side once you have turned it on, and see if power flows across the switch. If so, move on to the starter motor live, and so on. If power stops immediately after the battery, ie, with the live probe of your multi-tester on the kill switch and the neg one earthed, I would suspect the battery. It could show 12 volts, but it may have no current supplying capacity. I had this recently on my road car. 12 volts at the terminals, but not enough juice to open the central locking. I had to enter and exit via the tailgate!!!!!!!!!!
I hope this helps.