Doz, post up pic of label side of PSU. Ithink some of what is suggested here may be bollyox.
I can't imagine an XP era laptop is less than about 60W. If more than 6 years old (remember Vista came out 6 yrs ago), I'd expect it to be closer to 100W.
I would aim for an inverter at least twice the capacity, ideally 3x the capacity, and go for a decent one, as the cheap ones produce far from perfect sine waves (the good ones aren't perfect, but a lot better).
Also, using over simplified maths, 120W will be pulling 10A from battery - assuming 100% efficiency
- so a 50AH battery will last 5hrs. Only deep discharging like that, the battery will be destroyed quickly.
Going back to my earlier post, maybe a more efficient laptop, possibly with multiple batteries... ...or a tablet.