What was Vbatt when the laptop and inverter appeared to not play well together? And what other loads were present?
Laptops are designed to run off "dirty" dc power... they are run directly off batteries, after all. In fact, the converter/power cord you plug in, converts ac to dc, correct? So I would expect the laptop to be the last thing to create problems with a modified sine wave inverter.
However, if there is indeed a problem with the laptop's charging system, it has yet to be verified. So, again, other things need to be ruled out.