When William Henry Harrison died and John Tyler became President, the question arose as to whether Tyler was entitled to a full four years or if he was merely continuing Harrison's term. One argument was that the Constitution gives the President the power of a term of four years and upon becoming President, Tyler's executive power included a right to four years exercise. The prevailing argument was that the term is of independent significance. The four year term (with the slight adjustment of the XXth Amendment) goes forward in time unbroken regardless of who holds the executive power within that term. Several individuals could exercise exectuve power within that time frame (like Alexander Haig).

The term began at noon on Tuesday. Who held executive power? The Constitution says that "before he enter on the Execution of his Office" the President shall take the oath. Sounds pretty clear to me that the term began at noon, his ability to execute his powers began after he had taken the oath (roughly 12:10 that day).

Under the Constitution, the old president continues to hold full power through 11:59:59, and then power shifts at noon. Article II, Section 1 requires that the new president, before executing any duties, take a prescribed oath or affirmation.

According to Steve Benen at WM:

Post Script: Just for the record, Obama really was president after the first oath, and everything he did yesterday was legit. In 1789, George Washington was president for seven weeks before he'd taken the oath, but he still had all the authority of the office.

He links to a pdf here.
The relevant part is on page 458 under the heading, "Oath of Office".

So why wasn't Michelle holding Lincoln's bible this time?

Presumably they had to have it back to the national archives before they were charged an overdue book fee.

the one site I did reference indicated the oath should take place before the new President does anything, and doesn't represent the transfer of power.

Under the Constitution, the old president continues to hold full power through 11:59:59, and then power shifts at noon. Article II, Section 1 requires that the new president, before executing any duties, take a prescribed oath or affirmation.