It sounds like a head gasket to me. If you have white smoke coming from the exhaust, it is usually coolant. Have you noticed a kind of sickly sweet smell? If so, that's coolant you smell.
Oversimplified smoke color test:
white = coolant or water
blue = oil
black = fuel mixture too rich
As for not wanting to start, when you shut down the engine, the pressures in the cylinders will leak down to atmospheric. However, the cooling system will still be under pressure, blowing coolant into the cylinder. The heat in there will cause some steam, which can condense on the plug thereby shorting it out so there is no spark. This coupled with the partial loss of compression in the affected cylinders will prevent the engine from starting.
Some parts houses have a tester that will "sniff" your radiator to check for blown head gaskets. It uses some color change fluid that detects gasoline or exhaust products in the steam.