1st thing to ask is how old is the battery ? as if the alternator was damaged then this can have a knock on effect with damaging the battery
so if you haven't already then I'd consider replacing the battery
if this is OK then check the state of the battery wiring for clean and tight terminals and if thats OK then I'd do a current draw test
I'd first check the easy things like is the boot light or any other interior light staying on then check that the main battery connections are tight and in good condition also check the earth strap to the engine / gearbox.Next I'd check the current drain aspect, the best way to find what circuit is causing the excessive currant drain is to fit a current sensing multimeter in series with the positive battery lead on the car and the battery, or use a current clamp meter on the battery positive cable.
A typical current drain with everything off and un-alarmed should be around 0.05Amp and if its higher than this remove a fuse and re-measure, if measurement doesn't change then replace the fuse and remove the next.
Once you've isolated the circuit with the excessive drain check the wiring connections and plugs to components and the wiring harness that runs by the engine bay fuse box - the wiring harness chaffs / rubs through and gets damaged - but its not always easy to see so be careful when checking..
down the system voltage too far even with jump cables
one other thing to consider is that the immobiliser is faulty and preventing the starter from being enabled - however if the dash / ignition lights are on then this usually means that its off
If this is all OK then its possible the car needs a new starter motor
understood, thanks for all extra info
in that case I'd suggest to check the condition of the main battery earth connection as it must be clean and tight and do the same for the small earth wires that run out of the engine bay loom and are secured to the engine with ring terminals as these are the ECU specfiic earth connections
the excitation wave from the ECU to the alternator should be a square wave
this page here has an excellent how to for diagnosing smart alternators
this way you can check with your scope to see if the alternator is being sent the correct signal from the ECU
do you still need help?
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