[Tristan Lall]

Keep your screen brightness to a minimum, turn off the wireless radios, and set your computer to aggressively conserve power. It will draw far less than 85 W.

As an anecdote, I used to use a 5-cell, 8 A·h lithium polymer battery (5 × 3.7 V = 18.5 V) to drive a Pentium 4 Mobile laptop (which normally used a 95 W AC adapter with 19 V DC output). I rigged a barrel plug and an extension lead to the battery, and was able to get about an extra hour, or maybe an hour and a half out of it. (The computer thought it was running from AC, so it didn't take advantage of some of the meagre power-saving features in Windows XP, plus it probably tried to charge the computer's battery from the external pack.)

Any chance you can rig a system like this, that avoids the DC-AC-DC conversion?