Perhaps somebody can identify this issue. The car is a 2003 BMW Z4. The symptoms are:
Car wouldn't start last week
Jump leads did nothing
Push started the car in 2nd, engine starts.
Took The car for a drive, stopped the engine, started it. All fine
Came back next morning, car wouldn't start
Replaced the battery. Started the car in Halfords car park. Drove home
Started the car again last night. No problems.
Tried to start it again this morning and nothing. Battery near full charge.
Lights etc. still working
If I push start the car again now, drive round the block, the car will start normally again.