According to LDS doctrine, what is the source of God's power?

This might not satisfy your question, but I don't believe there is an answer that could fully satisfy your question.

First off it depends if your talking about Heavenly Father or Jesus Christ. Christ got his power from the Father. Here are a few references to back that up. (These aren't actual quotes, they're just small interpretations I found on a page on lds.org. You can visit the actual scriptures to see what they say)

Christ is called the Father because he was conceived by power of God: Mosiah 15:3.

the Father gives the Lord power to redeem men from their sins: Hel. 5:11 .

the Son received all power from the Father: D&C 93:17 .

In the case of Heavenly Father, I believe that he doesn't get his power from anywhere he is power in himself. He is a self-sustaining infinite power source. However, this is not doctrine, this is only what I believe.

Here are a few snippets of scripture where I get this idea from. Some of these scriptures are probably talking about Jesus, but Jesus's power originated from Heavenly Father so it still applies here. (These are actual quotes)

he hath all power unto the fulfilling of all his words: 1 Ne. 9:6

the Lord is able to do all things according to his will: 1 Ne. 7:12

the all-powerful Creator of heaven and earth: Jacob 2:5

he created all things, both in heaven and in earth; believe that he has all wisdom, and all power, both in heaven and in earth;: Mosiah 4:9 .

the Lord God hath power to do all things which are according to his word.: Alma 7:8 .

God has all power (not exact quote) : Alma 26:35 . ( Morm. 5:23. )

all-powerful God,: Alma 44:5 .

O Lord, that thou hast all power, and can do whatsoever thou wilt for the benefit of man;: Ether 3:4 .

Retaining all power,: D&C 19:3 .

So basically There is a recurring thought that god has all power and he created all things. Well human and mortal logic would tell you "something had to have created Heavenly Father, he couldn't have been around forever, something had to have been before him. Something had to have created him and thus given him his power." This doesn't have to be the case.

No matter what you believe, the idea that time has been around for infinity before now is basically impossible to comprehend and the idea that there was a beginning is also impossible to comprehend. If there was a beginning, what happened 5 minutes before the beginning? What was before the beginning that caused the beginning to happen? As you can see, these concepts are impossible to understand.

When god tries to explain things to humans who are infinitely less intelligent than him, he has to kind of beat around the bush for us to understand. So when the scriptures say "God has all power and created all things". This could mean that God truly created all things and all power. And would this mean he created himself? If so, then he was around before he was created, which makes no sense. He could also just be explaining a complicated God-like law of physics in a way that us humans would understand. Remember, God is only going to tell us what we need know.

In respect to how limited our human brains are, the answer to your question in my belief is that God doesn't get his power from anywhere, he is power in himself. He is a self-sustaining infinite power source. (whether something else created him and so that is the root of his power, I have no idea)

Again, this is not doctrine, this is only what I have reasoned.

Short answer to corroborate what the others have said: the name of God in the Old Testament, which is shown as LORD in the King James Version, and is translated as Jehovah or Yahweh (note: I'm not a Hebrew expert); and which is what Christ called himself in John 8:58 -- "I am", or "I am that I am", means the "Self-existent one" -- meaning his power, etc. comes from within himself. Which is what the other answers are trying to say in their answers. My point is that the Lord's Old Testament name suggests that very idea.

The Lectures on Faith answer this query very directly and eloquently. From Lecture 1:15:

By this we understand that the principle of power, which existed in the bosom of God, by which the worlds were framed, was faith; and that it is by reason of this principle of power, existing in the Deity, that all created things exist—so that all things in heaven, on earth, or under the earth, exist by reason of faith, as it existed in HIM.

And the next verse even goes so far to say (emphasis added):

Had it not been for the principle of faith the worlds would never have been framed, neither would man have been formed of the dust—it is the principle by which Jehovah works, and through which he exercises power over all temporal, as well as eternal things. Take this principle or attribute, (for it is an attribute) from the Deity and he would cease to exist.

So according to the Lectures on Faith, the source of God's power is faith. This makes perfect sense and is consistent and complementary with all other scripture.

I would highly recommend reading all of Lecture First (as well as the other Lectures) to get a thorough and deep understanding of God's power, His character, and many other important teachings about Him (and ourselves as His children). The Lectures on Faith are an indispensable scripture for understanding God's power and where it comes from.

Some people may say that the Lectures aren't scriptural, but that's actually false. They were a part of standard Church canon all the way from 1835 to 1921. You can see a copy of the above-quoted verses in the original Doctrine and Covenants. According to the Joseph Smith Papers website (which is owned and operated by the Church of Jesus Christ of Latter-day Saints):

[...] As the bipartite title “Doctrine and Covenants” suggests, the new book was made up of two parts. The first part, on “the doctrine of the church,”[11] comprised a series of seven doctrinal lectures on the subject of faith, first prepared as a course of instruction for the School of the Elders [commonly known as "the School of the Prophets," which was taught by Joseph Smith] held in the second Kirtland printing office in the winter of 1834–1835.[12]

[...]

The second part of the Doctrine and Covenants contained the “covenants and commandments of the Lord,”[15] or revelations. Inasmuch as the revelations made up the majority of the volume and the volume’s title indicated that the texts therein were “carefully selected from the revelations of God,” it is curious that the revelations were placed in the second part of the book.

(taken from the Historical Introduction to the 1835 D&C)

It would, therefore, appear that the Lectures on Faith originally comprised the "Doctrine" of the Doctrine and Covenants (the other revelations comprising the "Covenants"). It is a mistake to consider the Lectures non-scriptural or non-doctrinal. They were only removed as the result of a fairly arbitrary decision by a committee in 1921. For further details on its removal, see The 'Lectures on Faith': A Case Study in Decanonization by Richard S. Van Wagoner, Steven C. Walker, and Allen D. Roberts. Suffice it to say, this removal did not follow the law of common consent. No general vote of the church was taken to excise this portion of scripture from the standard works. So I would argue that the Lectures are still scriptural, despite claims to the contrary.