Will a corroded battery cause your car not to start sometimes?

YES!!!

Replace the car battery.

The white corrosion seen on one of the battery terminals, is also inside the battery.

The internals of a car battery contains lead plates , copper platres and sulphuric acid. During the (dis)charging process the sulphuric acid combines with the lead to form lead sulphate (The white corrosion). When sufficient of the white corrosion builds up inside the battery on the lead plate , it will eventually touch to copper plate. Whereupon the battery discharges and will not re-charge. The battery is //??@@#@!!! XX . So replace the battery.

Sometimes, during the sulphuric acid /lead reaction hydrogen gas is liberated, if an electric spark occurs in the gas , there will be an explosion. So definitely change the battery!!!!!