Screen goes black/inverted/garbage, fixed after sleep

Screen goes black/inverted/garbage, fixed after sleep

I have a "late 2010" MacBook Air 13" (C2D 1.86GHz, the version without the backlit keyboard). It has not been spilled on, suffered any trauma, etc. Was working fine (sitting on a stand, plugged into a 20" Dell monitor) and today all of a sudden the laptop screen (but not the Dell) went sort of inverted, with some garbage.

Since then, I've been using the laptop by itself, and it's done it a couple of times since then. Every time the effect is a little different; the most recent one, the screen went solid black with some red pixels. Usually it looks more or less like this:

Picture showing the screen malfunction

If I put the computer to sleep (either by power key then 's' key, or by closing the lid, waiting until the backlight illuminating the Apple logo switches off), the problem is fixed immediately after the computer resumes from sleep (open the lid or hit a key on the keyboard).

I don't think it's a loose cable, since the problem is fixed without moving anything but simply sleeping and waking the computer. Thoughts? (The motherboard was replaced by Apple a couple of years ago, it was losing all settings and going back to 1970 every time the battery ran out while the computer was sleeping. But no problems in 3+ years of fairly constant use...)