Probook 450 G2 shuts down hard, randomly.

[BryanW1]

A few days ago, my 2 year old (fan failed already under warranty) Probook 450 G2 has started to shut down.

By this, I mean you can set it on a table, and it will randomly shut off as if you pulled the plug. Restarting the unit gives the "Windows did not shut down properly" screen, and upon resuming, the machine takes a long time to boot and the audio does not work. I can plug headphones in, and get a faint crackle if something plays. So far, the audio will come back after a short time, but this last shutdown it has not.

The unit is running the version of Windows 7 that came with the device, all drivers are current, and none of the extra software has been installed save that which is required by the system. Event log shows nothing other than a hard shutdown, and Windows does not show any troubled devices in system. I'm pretty sure it's not an overheat situation, as I can sit there and play games all day with the fan spinning hard, and nothing happens.

This problem is completely random. I left the unit running overnight with some heavy graphical processes running, and nothing happened. Today, I turn it on, and 10 minutes later in the middle of just sitting there it shuts off.

Is this thing repairable, worth repairing, or is there something I've overlooked? What say you?

edit: Some new information.

I've tried some extensive (read song and dance) troubleshooting with the battery and power systems, as this problem seems to be related somehow:

The laptop will randomly shut off on battery, on AC, or any comibination thereof (charging, etc.)

The battery seems to drain very quickly when the laptop is off - it goes to no charge overnight (sometimes!)

If the sound works, the unit responds to pressing the power button (give the shutdown? dialogs)

If the sound does not work, the power button does not work.

If the battery is out, the unit will not turn on with the power button.

If the battery is out, the unit will turn on as soon as the laptop is plugged in.

If the sound does not work, booting the machine without the battery and then plugging the battery in will sometimes bring it back - the power button starts responding at this time as well.

To be fair, the battery has shown odd problems since day 1 - there have been a few times where the battery drained to 0% charge overnight, and the problem of the machine turning on with the AC adapter may have been there for a long time - I simply didn't know it because the battery was always in.

I'm thinking that there's something wrong with the battery as well as the mainboard. Any ideas?