Chapter 38 Hezekiah's Illness And the Wondrous Sign From God Guaranteeing the Deliverance of Jerusalem.
This was prior to the visit of ambassadors from Merodach-baladan (Isaiah 39:1) and thus chronologically prior to Chapter s 36-37. The chronological transposition suits Isaiah's purpose. He wanted to bring the threat of Babylon in juxtaposition with the second part of the book where Babylon is revealed as finally destroyed. But it would not be understandable in 2 Kings unless 2 Kings was influenced by Isaiah. Thus it is unlikely that 2 Kings can be primary. But it is also unlikely that 2 Kings is simply an expanded version of Isaiah 36-39. The explanation that fits all situations is that Isaiah also wrote a longer version of the events described here at the time that they happened, which was incorporated in 2 Kings (2 Chronicles 32:32), while also being summarised here.
Chapter s 38-39 cap the first part of the book. They demonstrate that Yahweh did indeed give a wondrous sign of His willingness to deliver a member of the Davidic house when he was acting on behalf of his people. Ahaz had refused such an offer (compare Isaiah 7:11-14), but now He was giving the house of David another chance. Here Hezekiah was to see that the sun performed Yahweh's bidding. But instead of this resulting in Hezekiah trusting in Yahweh, he turned rather to Babylon for help. This final failure to trust Yahweh completely, revealing even the good king Hezekiah and his descendants in a bad light as unsuitable to be the Coming King, resulted in his being cast off. The final verdict is that in fact his descendants in the Davidic house will not achieve glory, but will rather be led into humiliating captivity and prevented from bearing children. So all Isaiah's exhortations to Judah/Israel and to Hezekiah had proved in vain, just as God had said they would at his inaugural call (Isaiah 6:9-10).
This then leads on into the second part of the book, where the emphasis is not on the coming Deliverer as a member of the Davidic house, but on the humble but glorious Servant (compare ‘David My Servant' - Isaiah 37:35), although as also introducing the ‘sure mercies of David' (Isaiah 55:3). He is still a greater David, descended from David, or the sure mercies would not apply, but not a crowned king in an earthly sense. Rather he is to be essentially Yahweh's Servant (Isaiah 42:1-4; Isaiah 49:1-6; Isaiah 52:13 to Isaiah 53:12).