Ever stirring in the depths of the heart is the desire for Well-being, for Truth, Beauty, and Goodness—the aspiration after some, thing more blessed, true, beautiful, and good than can be realized here below. This is that longing after something absolute and sufficient—the immensum, infinitumque—which is so often breathed forth with passionate earnestness in the pages of the thoughtful men of every age of the world. With nothing finite can this longing after blessedness be quenched; restless and unsatisfied, we turn from every good which this world, which this life, can yield. We aspire; we seek; we gain the objects in which we hoped to find full repose and contentment; but ever with their possession we fail to find that perfect rest of heart. This world and all that it contains cannot fully bless the human soul. There never was a human being who found in the world a happiness fully corresponding to his desires, a well-being answering to his ideal; and in the nature of the human soul it never can be found. Ever at the end of the longest search, of the widest experience of what this world can give, has burst forth the yearning cry: Who will show us any good? a cry that must be ever one of hopeless yearning until we raise our minds to God, the Absolute Substance and Source of Truth and Beauty, of Goodness and Blessedness. Then we cry with hopeful faith :— Lord, lift thou up upon us the light of thy countenance. Admit the being of a God who implanted these infinite desires in the human heart, and then we may find a ground of hope.
William Whewell, "The Moral Argument for the Existence of God", On the Foundations of Morals, (pp. 147-148). The quotation is from Psalm 4:6 (KJV). Whewell goes on to add the yearning for the permanence of this blessedness (i.e., immortality).
This is the fourth of the four strands of Whewell's moral argument. I have given representative passages for the other three, dependence, gratitude, and conscience, already. Each of the four is an inductive argument in Whewell's sense of the term -- given phenomena for explanation, we 'superinduce' a concept on them to explain them. The reason for doing a multi-strand argument is (arguably) that one of Whewell's marks of progress in inquiry is consilience -- that is, the 'jumping together' of different kinds of phenomena under one explanation. Progress in knowledge, in Whewell's philosophy of science, consists in great measure in rising up to more and more architectonic concepts that unify more and more of the phenomena we experience and conceptualize. Each strand merely suggests; but the fact that one explanation can harmonize the various strands makes it inductively strong (again, in Whewell's sense of induction). This is probably why he also treats the moral argument as something that goes with physical arguments: just as this explanation harmonizes and accounts for physical nature, so too it harmonizes and accounts for the sentiments, dictates, and desires of our moral nature. The moral argument is not made to stand alone, but as a major element in a larger cumulative argument.
It's notable that the gratitude and the conscience strands clearly trace back to Kant, although since Whewell has a somewhat different epistemology and metaphysics than Kant, we should perhaps not overassimilate the two. Whewell's conception of conscience also owes more to Butler than it does to Kant. I suspect that the dependence argument has roots in German Romanticism; Schleiermacher's On Religion is a genuine possibility, in terms of arguments that clearly do appeal to a sentiment of dependence in this context and that Whewell stands a chance of having known either directly or indirectly. I do not, however, know of any evidence that clinches that matter.
The infinite desires strand above is almost certainly rooted in Plato. Whewell will later bring out a work called The Platonic Dialogues for English Readers, which are an interesting experiment, in which he tries to make the dialogues more intelligible by mixing translation, paraphrase, and commentary in a unified way. That he put so much time into doing this is a certain indication that he rates Plato as a very important ally in his struggle with the utilitarians, just as his active work in supporting Butler does the same for Butler. The discourse on the moral argument is so early in Whewell's career, though, that it is difficult to be more precise.