Dust can get inside computers and monitors (and other electronic equipment as well). I've even see spiderwebs in them! This can help block air flow, especially if the junk has been inside for a while -- as might be in a six year old monitor. Couple that with blocked vents and you might reach the ignition point of a pillow.

Consider, too, the age of the monitor. Computer innards DO fail, and not necessarily quietly and with a whimper. I've seem 'em do everything but burst into flames, and I'm not ruling out that they could. The moral is: blow the dust out with "canned air" every so often -- and DON'T use a dust cover unless you're in a very dusty environment (and if you must use one, wait several minutes after you power off for the thing to cool off).

But if there were pillows there that weren't there in the morning, I'd suspect maliciousness. How old were the pillows? Some older ones had a much lower ignition point than more recent ones (remember how Stan Rogers died?). I'd look at who might have been in the house when I was gone if you're certain about the pillows.