Diagnosing alternator help

[MadProfessor]

Hi guys

I recently bought a luxo-shed of a 1996 LS400. It's been running fine until yesterday when all of the warning lights would come on whenever I didn't have the accelerator pressed, but would instantly go off whenever I gave it a little gas. This morning the car wouldn't turn over although the lights and other electrics would come on (e.g. radio). This afternoon nothing at all electronic works e.g. not even the remote central locking.

Obviously there's a fault right now with the battery being dead but how do I determine if it's just the battery or instead the alternator not charging the battery.

The power of Google reveals that a common fault is the power steering pump on these cars leaking onto the alternator.

Any tips of how to differentially diagnose the fault.