Hi Susan
The Cam belt snapping would certainly stop the engine. It is this belt that keeps all the bits moving at the right time an in the right sequence. Whereas a leaking head gasket USUALLY just make the poor thing shed water out of the exhaust and sound asthmatic.
Often when it snaps much damage is done as a valve can come into contact with a piston. However some engines do "fail safe" but I do not know about the Toyota.
Good engines though - very strong - as long as you change the oil regularly and get them serviced.
However what can happen is water seeps into a cylinder bore and if it stays there, this can stop the engine because a gas can be compressed but a liguid cannot. So if the piston coming up in the bore is trying to squeeze water it will not be able to and so the whole thing stops. Normally the piston comes up, compresses the air and petrol mixture which explodes via the spark plug and this explosion forces the piston down which ultimately turns a shaft which goes onto turn the wheels.
The symptoms are very similar to snaped cam belt, which incidently should be changed regularly as per the handbook.
Did the engine not start one morning or after a long period of you not using it? The reason I ask is that it can often take a long time for the water to seep accross into the cylinder to such an extent that the engine cannot work. What usually happens is that very small amounts of water do build up but as long as the car is run frequently this is simply ejected out of the exhaust on starting. Starting can be difficult and a bit like a rather smelly sauna if it is done in a confined space.
I do recommend that you check that the garage has made sure that your cooling water is NOT contaminated with exhaust gases. This will make sure that the correct problem is being fixed.
Like Ray, I wonder why the radiator is being changed - it may need changing anyway and not be part of the problem.
When you collect the car make sure you rev it hard and check for steam in the exhaust. Then monitor the water level to see if it is falling. If it still does then you still have the same problem but the garage has got you to pay for a lot of new unessassary bits. Make sure they now that if it is not right you will be bringing it back.
INCIDENTLY - on this subject when I first had my caravan serviced I was told that my Fridge would not fire up on gas and that it would be about