How to debug a kernel panic? Ubuntu 14.04

So, I have been having kernel panics. My computer will suddenly come off and then a dmesg like output shows on the screen. The first two lines read

[20352.651631] BUG: Unable to handle kernel NULL pointer dereference at 0000000000000028
[20352.651667] IP: [<ffffffff8158a7bb>] input_event+0x2b/70

And the last two lines

[20352.662214] Kernel panic - not syncing: Fatal exception in interrupt.
[20352.662214] drm_kms_helper: panic occurred, switching to text console

Here is a picture:

I would post directly but it doesn't let me. Also, I can't find the dmesg output. I ran

sudo grep -nri panic /var/log/
zgrep -ni panic /var/log/dmesg.*.gz
zgrep -ni panic /var/log/kern.log.*.gz

All I got was registered panic notifier but nothing about the crash.

Anyway, it has happened a few times this past month, and I haven't been doing anything in particular that I can see for this to happen. Usually I'm browsing the web or watching videos or writing up homework and suddenly, crash. Screen goes dark, text output, and I can't do anything until I manually switch the computer off and on.When it comes back on, everything seems to be perfectly normal and it won't crash again for a week or so.

I have also been reading but I can't make much out of it. I'll go over it with some more detail, but I'd really appreciate some advice on how to get started with the debugging.

EDIT

It happened again. I've posted a picture and corrected what it said. I finally have time since it's the weekend. I'll run memtest and try to reproduce the panic at home. Just to be clear, my computer boots and works just fine---nothing weird happens that I can notice, until it crashes, that is.

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