Why did God only hear the Hebrews' cries during the service of the king's death?

[Robert]

Contributor "gib65" wrote: 

[...] why did God wait for 400 years before emancipating them? [...]

The years of slavery were prophesied in the "vision (of Abraham) between the parts" to be 400 years: Genesis 15:13. 
The "habitation" in Egypt is stated to have been 430 years: Exodus 12:40. 

If by the contributor's word "emancipating" this is intended to refer to the Egyptian slavery, the number of "400" years is incorrect; the number of years under the Egyptian slavery was far less than that.

The reader can see an analysis of the number of years of the slavery, here: 
https://aish.com/duration-of-slavery-in-egypt/

The total time the Children of Israel stayed in Egypt can be calculated to have been 210 years (see Rashi commentary below), 
and of those 210 years the slavery was between a minimum of 86 years and a maximum of 116 years. 

Exodus 12:40:
[...] the habitation of the children of Israel, that they dwelled in Egypt, was four hundred and thirty years.


Commentary by Rashi:

that they dwelled in Egypt:
after the other dwellings in which they dwelled as foreigners in a land that was not theirs. — [from Mechilta]

was four hundred and thirty years:
Altogether, from the time that Isaac was born, until now, were 400 years. From the time that Abraham had seed [i.e., had a child, the prophecy] “that your seed will be strangers” (Gen. 15:13) was fulfilled; and there were another 30 years from the decree “between the parts” (Gen 15:10) until Isaac was born. It is impossible, however, to say that [they spent 400 years] in Egypt alone, because Kehath [the grandfather of Moses] was [one] of those who came with Jacob. Go and figure all his years, all the years of his son Amram, and Moses’ 80 years; you will not find them [to be] that many, and perforce, Kehath lived many of his years before he descended to Egypt, and many of Amram’s years are included in the years of Kehath, and many of Moses’ years are included in Amram’s years. Hence, you will not find 400 years counting from their arrival in Egypt. You are compelled, perforce, to say that the other dwellings [which the Patriarchs settled] were also called being “sojournings” and even in Hebron, as it is said: “where Abraham and Isaac sojourned (גָּרוּ) ” (Gen. 35:27), and [Scripture] states also “the land of their sojournings in which they sojourned” (Exod. 6:4). Therefore, you must say that [the prophecy] “your seed will be strangers” [commences] when he [Abraham] had offspring. And only when you count 400 years from the time that Isaac was born, you will find 210 years from their entry into Egypt. This is one of the things that [the Sages] changed for King Ptolemy. — [from Mechilta, Meg. 9a]

Link (click the "Show Rashi" button - Sometimes the Rashi is not shown even when this button appears to be active, so please click it anyway to make certain it works !):
https://www.chabad.org/library/bible_cdo...ter-12.htm

Contributor "gib65" also wrote: 

[...] It suggests that only upon crying at the service did God hear them, and only because it was a service (a religious ceremony). [...]

It was nothing to do with any ceremony of the king's death. It was that the king dying caused the children of Israel to concentrate upon their predicament, and they cried out to G-d.

The following was the result of their crying out to G-d; causing G-d to curtail what could have otherwise been a longer enslavement:

Exodus 2:24:
God heard their cry, and God remembered His covenant with Abraham, with Isaac, and with Jacob.