Right, after spending the 300 quid to get the damn thing through its MOT, today the following happened. Please bear in mind that I got all this second hand, she had the car.
It started fine once it had been defrosted - she parked up, locked the car with the keyfob remote then returned about five minutes later. She tried to start it, but all that happened was the alarm went off. She stopped the alarm with the panic switch thing under the glovebox. She tried to start it again, and this time the alarm went off briefly then it died, like it was losing power. At time of writing, she is waiting for Green Flag to come out.
Any advice (that is constructive and doesn't mention women drivers) greatly appreciated.