Renult Megane T Plate will start cold but not if used stop then start??

Renult Megane alize secnic T Plate 1999 43k on clock, problems starting car was told it was the battery so got new battery but still at times wont start, loses all power knocks the clock out also milage currently used not actual, will alwasy start if left to go cold but if going out stop at the shops for 5mins then try to start nothing!!!!!! All lights heater wipers work, Petrol gaughe goes way up to full! but just no turn over!!