Old truck, new everything -- won't start after sitting. Why?

Ok, first, I know this is an old truck. But, I've had extensive work done on it:
tune up kit (plugs, wires, cap), a rebuilt 2-barrel carb installed, timed by a
good mechanic. The fuel pump works ok I was told. When I asked the
mechanic if there were anything else I could do, he replied honestly, "It is
what it is." Ok, my question is, if all of the above has been done, what is the
difference between that engine and one that is much newer? In other
words, why is it so difficult to start, especially if I let it sit for only a few days
(nearly run down the battery then). What else can I do to/for the engine?
Thanks.