There's dozens of parts that all have to work and you know we can't diagnose the bad one over a computer. Have you checked for spark? Fuel pressure? Does the engine sound normal when it is cranking? Crankshaft position sensors and camshaft position sensors often fail by becoming heat-sensitive, then they work again when they cool down for about a half hour. To have sat for a couple of hours, then not driven far enough to get warm yet is more typical of a broken timing belt, but there are a lot of other things to look at before assuming the worst. Have you checked for diagnostic fault codes?