Car cuts out under breaking

I've had my vectra for around 5 months now, and it's ran fine up until now (a bit temperamental in hot weather but other than that, ok).
Last week my hazards came on in the warm whilst it was parked outside work, and stayed on all day, running my battery flat. Since then, I can't lock/unlock using the fob, and the engine has been cutting out regularly. Anytime I am breaking firmly, pulling up for a junction, the car will just cut out. It will sometimes start up again if I put my foot down straight away, but if not, it needs turning over again.

I've noticed the engine management light is on a lot now too, I managed to drive about 5 miles with the engine management light off, without the problem occurring, but if the light is on, it will make it to the next junction and do it again.

Can anyone help??