Hi, Welcome to Just Answer!
The first test that needs to be performed is a compression test. This is how you determine if the head gasket is blown. The initial description of what happened is classic to a blown head gasket. Take the guess work out of it and let the compression test prove it. All cylinder pressure should be within 20 psi of each other, if not... you have a blown head gasket or cracked head(cracked head is not very common).
If the starter just doesn't turn over then it can be tested by checking for power at the starter with the key in start position. If it has power and does nothing (no click, no nothing) then the starter needs to be replaced. If it gives a hard click. then the engine may be vapor locked from coolant entering the cylinders.... so back to the first thing first. Have a compression test performed(which should have been the first thing done).
If the mechanic says he can not perform this, then you need to take it to a different shop.