M6400 strange battery/GPU problem

My M6400 has recently been demonstrating strange crashes while on battery. On AC, it'll run like a champ for hours, but if I unplug it from the wall it'll crash within minutes of playing a 3d game or playing a video. The crash screen looks very strange - light blue vertical pinstripes on a dark blue background. There is no record of the crash in Event Viewer, just a record of an unscheduled shutdown. I've tried with Windows 8.1 (Microsoft supplied WDDM 1.1 driver) and Windows 7 (Dell driver released this month), with the same results. The GPU is a Firepro M7740, which has served me well since I upgraded it a couple of years ago. Personally, this doesn't bother me that much since I'm usually tethered to a wall anyway. However, I intend to sell it to finance some upgrades for my new (to me) M6600, so I'd like to get it working properly. I could put the old Quadro 2700M back in it, but I'm not sure that's the problem, and it might diminish what little resale value this old warhorse has. I'm not sure if this a GPU issue (most likely) or something to do with the battery. Any suggestions?

Specs below...

Dell Precision M6400
Intel Core 2 Quad QX9100 (ES)
8GB DDR3-1066 RAM
500GB WD Scorpio Black
ATI Firepro M7740 1GB
1920x1200 LCD panel

 

Most probably it is something to do with the battery. It might be on its way out, is faulty or no longer able to retain charge. How old is it?

 

I've had the laptop for a couple of years, and never replaced the battery, so it's at least that old. I hardly ever use it, but it's to be expected that it would wear out. However, I wouldn't expect crashes, just diminished capacity. Have you seen this kind of behavior from old batteries before?