I was thinking it might be an issue with the starter button itself. All the cars power runs thru it.... so if one of the nuts underneath it is loose you wont get clean power to either the starter motor or the whole system..
Once the engine is running, you can remove the battery (disconnect it at the starter button) and the alternator/generator will create enough power for spark and light.
But, if you say you replaced your floor starter button and had no initial improvement, my guess is that you may have an earthing problem. Check your earths where they connect to the body (next to the battery and under your clutch cover) - unbolt them, sand or wire brush the mating surfaces then reconnect.
Connections will still work if they are dirty, but somewhat inefficiently. The current wil "arc" across a dirty connection if possible...... and sometimes it wont even do that. More so when the battery hasnt recharged fully from the last time you started the car.
If none of that helps, its time to inspect your wiring loom. Pay close attention to locations where the loom passes thru holes on the steel work (eg: behind the speedo) or under the metal fastening tabs (eg: under the dash and under the windscreen wipers). Steel panels can cut thru wiring looms thru vibration, leaving exposed wires that could short each other out. I have had this problem in a previous mini and was forced to replace the whole front loom.
Fun and games, yeah right.
PS.... if thats your mini in your avatar..... seen it and like it
