I have a Renault Megane 1.4 on a 54 plate?

Firstly my car was left standing for a long time and the battery died. I replaced this with a brand new one but every time i start it now it cuts out straight away unless i put a lot of revs on it, any ideas?
Also last week the engine light and the service light came on at the same time. There hasn't been any change in the performance of the car although i only drove it to recover it home. Is this something that i should be worried about?