Shemot #1: Vayakam Melech Chadash Al Mitzrayim

In the first perek in Shmos, we read that a new king began ruling over Egypt. Shemot 1:8:

ח וַיָּקָם מֶלֶךְ-חָדָשׁ, עַל-מִצְרָיִם, אֲשֶׁר לֹא-יָדַע, אֶת-יוֹסֵף.

8 Now there arose a new king over Egypt, who knew not Joseph.

However, this pasuk is at least three-ways ambiguous, and the midrash rabba on Shemot advances at least three explanations.

1. The simplest, peshat explanation is:
וַיָּקָם is the intransitive verb meaning arose.
מֶלֶךְ, king, is the subject of the sentence.
חָדָשׁ, new, is an adjective modifying the subject מֶלֶךְ, king.
Thus, "A new king arose over Egypt, who knew not Yosef."

An intransitive verb is one that operates only on one noun, its subject. Thus, "He grew," meaning "he became bigger" uses the intransitive verb grow, while "He grew tomatoes" uses the transitive verb grow.

2.
וַיָּקָם is a transitive verb. The root qym means decree, thus "He decreed/established."
מֶלֶךְ, king, is the subject of the sentence.
חָדָשׁ, new, is the object of the sentence, or else is an adjective modifying the implicit object "decrees."

Thus, "The king decreed new [decrees] on Egypt, which did not recognize [the historical importance to Egypt of] Yosef."

Rashi cites both explanations:

8. A new king arose. [There is a controversy between] Rav and Samuel. One says: He was really new, and the other one says: His decrees were new.

but people do not realize that these two alternatives are the result of two ways of parsing the pasuk, two understandings of the verb וַיָּקָם, and two understandings of the function of the adjective "new." Rather, they think it means that he is called a new king because he was an old king who acted as if he was a new king. I feel that half the fun in midrash is figuring out the derivation of midrash.

{Note the stama demidrash asks on #2 the meaning of "who did not know Yosef" if it was the same king, and answers that he made himself as if he knew not Yosef at all. I don't think this is necessary, but is an acceptable explanation of the rest of the pasuk.}

3. There is a third explanation, attributed to the Rabanan.
וַיָּקָם is an intransitive verb, arose.
מֶלֶךְ, king, is not the subject of the sentence, but part of the predicate.
חָדָשׁ, new, is an adverb, modifying the verb וַיָּקָם rather than the noun מֶלֶךְ.

Thus, "He arose anew as king, because he [agreed to] not know Yosef.

The Rabanan give the following narrative corresponding to this parse. The nobles came to Pharoah and ask that he array the Egyptians agains the Hebrews. He refused, saying "we are eating of theirs, for if not for Yosef we would not now be alive." As a result, the nobles removed him from power. After 3 months, he agreed to be with them in their counsel, and they restored him to power. Thus, וַיָּקָם מֶלֶךְ-חָדָשׁ.

None of the parsings I give are explicitly written in the midrash. You must reconstruct the parse from the opinion, but I think it is clear that this is how they respectively parse it.

Update: One could suggest a fourth interpretation of the pasuk: take מֶלֶךְ to mean council. Indeed, Jastrow links king and counsel as the same meaning - a king is king because he is head in counsel. Here is one smippet from Jastrow, available in this pdf.

melech - jastrow pg 791

Thus, a new counsel arose in Egypt, namely, not to recognize Yosef. {or, one which did not recognize Yosef.}

This fits well into the context:

ט וַיֹּאמֶר, אֶל-עַמּוֹ: הִנֵּה, עַם בְּנֵי יִשְׂרָאֵל--רַב וְעָצוּם, מִמֶּנּוּ.	9 And he said unto his people: 'Behold, the people of the children of Israel are too many and too mighty for us;
י הָבָה נִתְחַכְּמָה, לוֹ: פֶּן-יִרְבֶּה, וְהָיָה כִּי-תִקְרֶאנָה מִלְחָמָה וְנוֹסַף גַּם-הוּא עַל-שֹׂנְאֵינוּ, וְנִלְחַם-בָּנוּ, וְעָלָה מִן-הָאָרֶץ.	10 come, let us deal wisely with them, lest they multiply, and it come to pass, that, when there befalleth us any war, they also join themselves unto our enemies, and fight against us, and get them up out of the land.'