How do you find out why T3-M4 voice-locked the astrogation computer and..

I do not think that you can find out exactly why he voice locked the astrogation computer. However, if you have played Star wars: Knights of the old Republic, then you will know that T3-M$ was actually Darth Revan's droid. In fact, HK-47, the droid that you have to repair, was his as well. Near the end of the game, Darth Revan traveled to an area called the Star Forge. Now, the Star Forge is like a key to ultimate power. However, you can only get that power if you were with the dark side. So, in order to prevent future Dark Lord's, and victims from going there, Revan erased HK-47's memory, and he told T3-M4 to lock the astrogation chart when ever someone got curious. There is no way to un-lock it that I know of, so sorry, but hey, unless you know why he locked it.

Hope this helps.

How do you get unit T3-M4

From what I know, it is not possible to unlock it, as previously stated. However, if I do recall, you can find out in the story: "Revan", if you haven't already.

Spoilers, if you haven't read Revan

I also write this here incase you do not wish to read Revan. There is no definite proof, but with what they say in both the book and KotOR II, it implies the travel to Nathema, the Emperor's (of the True Sith Empire hidden in the Unknown Reagions) homeplanet.