2000 mazda 626 over heated and turned of but not before white smoke came out tail pipe , now won't turn over , sounds really rough when I try.

It will not start because you now have a major compression leak and the most likely cause is a damaged head gasket from running the engine in an overheat condition. You may also have cracks in the cylinder head and the cylinder head may be warped. This will not be a cheap repair.

White smoke is caused by radiator coolant entering the cylinder. The white smoke is steam because the coolant is 50% water.. Any amount of radiator coolant that enters the combustion chamber by any means will produce a white steam that will be present in the exhaust. As mentioned, the coolant will most likely be getting into the combustion chamber via the damaged head gasket.

You may also find coolant has entered the lubrication passages in the engine and contaminated the oil which will be evident on the oil dipstick, especially the colour of the oil. You might also find there is some cross oil contamination in the coolant which will show easily because it won't mix with the coolant.

Don't try and start the engine. You will do more damage if you do.
The cylinder head will have to be removed and checked for straightness and checked for any cracking. In the least it will most likely be warped from the overheat and if so it will need to be machined. The valves and valve seals will also need to be checked. Once the cylinder head has been sorted the engine block will need to be checked for straightness and for any signs of cracking. A new head gasket will need to be fitted before the cylinder head can be refitted.

It probably does have a blown head gasket unfortunately. And it will not crank? or just not fire up?

If it will not even crank, the motor may have seized. If so the damage may be so severe that another motor from the wreckers yard is the best option, unless you are handy with a wrench..
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