Suddenly, I can't log into my session anymore?
 

Distribution: Elementary OS Luna (based on Ubuntu 12.04 LTS) x64

The computer starts and bring the login screen seemingly without error. If I input my password and hit Enter, the screen flashes black with some text on it, then the login screen comes back. I can't read anything on what may be error messages as it's too brief. It does look similar to the text I have when I shutdown properly.

My session and any other, including guest, are unavailable this way.

I can log into TTY and do whatever needs to be done. When I do login with the command line, no error is printed. I read somewhere on the internet that .xsession-errors may hold a clue as to what may be broken, but I can't decipher it. You can find it here.

I tried using the previous kernel, but it didn't help.

Before it was broken I wanted to connect an ipad to the computer and solve the trust bug. Using the package provided gave me a dependency problem: libusbmuxd2 couldn't be installed on my system, and I went out of my way to download and install an incorrect version of it. It was obviously a dumb move but I'm surprised it broke my system as much as it did. I removed the packages as best as I could but it didn't solve the problem.

I am now clueless as to what I can do. What do you think?

From the error messages it seems your system is very unhappy with the state of Gnome. Gnome is what you use for a desktop environment, yes? One possibility would be to reinstall gnome and see if that solves the problem.
jdk

Well, elementaryOS doesn't use Gnome so I'm not quite sure it would solve my problem. From what I can gather from blinking very quickly at the error message it seems the OS can't write something. Is there any place where I can gather log of what's happening at session close (as it seems this is what I'm witnessing, my session closing with errors)

Then I don't understand why the error messages contain repeated references to a gnome-settings-daemon. Do you?
If you're not using gnome then what DE are you using?
jdk

It's Pantheon, a new DE specifically made for this project.

Same advice: try a reinstall and see if that changes something. Is it possible that Pantheon is buggy?
jdk