Ford mondeo mk3 2.0l Petrol Electrical fault?

[Plasmodium]

Recently acquired a mondeo mk3 2.0l petrol that had been sat for a year or two on a neighbour's drive. When we first tried to switch the car on, it wouldn't start (to be expected after sitting for s so long) and it all the electrics (lights etc) would flick rhythmically in time with eachother.

The battery was replaced and it seemed to cure the problem for a while. Most of the time it will start either first or second attempt, but when it does start, it will often die after a couple of minutes, and when you come to restart it, it won't start and the rhythmic flickering and clicking returns. Any ideas on what this could be? Not really willing to spend a lot on it as it was a freebie and has a lot of miles (170k).