Sounds like you have a bad battery that wont hold a charge. Or maybe a bad charger.
Many nokias use the same batteries and chargers as the 6010. If you know someone with similar equipment try using a different battery or charger and see what happens. If not, it might be under warrenty from where you bought it. Worse case scenario, you can replace it for $20 on ebay or a walmart for $40 and put your old SIM in it.

Hi,
My nokia 6010 won't switch on. When the batt ran out I charged it but now it won't switch on. When I try to it goes off with a flash on the screen....dont know why. Plase adivse. Thanks much