Hi and welcome to the forum, sorry to read of your problems.

I think the door open light only refers to the boot, it does on my mk1 MGF.
That means that the system thinks the boot is open so turns on the boot light.
The sensor is part of the boot latch.
It is also possible that you are getting a short through the boot hinge wiring which causes the system to think the boot is open.
The boot light will drain the battery in a couple of days.

As for the battery itself I would check it with a good old fashioned multimeter.
If it was completely flat a regular battery charger will not be able to recharge it properly.

If you connect your car to another using jump leads you should get full ignition lights even if there isn't enough oomph to start the car.

Let us know how you get on.

James

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