Blank screen after an interval; maybe related to laptop power supply?

[Dartme via arch-general <arch-general@xxxxxxxxxxxxx>]

I turn on my laptop, sign in (Linux getty), and use the laptop for a couple
minutes (no graphical applications), then the screen goes black and the
machine does not appear to respond to any user input (CTRL+ALT+F2, etc.).
The only recovery I have found is to hold the power button and restart. The
logs show nothing. When I use the computer without the power supply plugged
in, the problem doesn't manifest. I'm using a Dell Precision M 4700.

Any suggestions? What should I be looking at to begin diagnosing the
problem?