NOW I see you DO have jump leads.... so forget above - just to save typing you could start by connecting red jump lead from battery live to lead that goes off to starter connection - should spark and churn EDIT - Earth jump lead is connected fine in 2nd pic but better off clamping somewhere on engine if you ever want to get the best out of a battery. Possibly not even needed now depending on how you get on with red jump lead connection.
Chris I actually love you (and all the others that helped)! IT WORKED! So new starter relay it is then!
What have you done? Have you just by passed the solenoid, if so it's a solenoid you need to replace. Steve Before you replace anything double check the connections and particularly the small white plug to the rear of the solenoid.
In your first photo to the right of the battery tray there is a yellow solenoid which says Hitachi on it, to the rear is a small plug which is a common problem for corrosion and generally poor fit, clean it tighten the connectors and secure it with a zip tie. A poor fit will stop the starter working. Steve
Don't throw the old one Clapton, it could have been the little plug connection so might be a useful spare in the future.
It's always a good idea to put a cable tie around the starter solenoid to stop that little white connector going adrift. My 4s has the same type solenoid and it stays in place a lot better with a little cable tie. Good trouble shooting there mate. I thought for aminute it might be a starter motor that needed brushes. As I had that recently too A