What are the voltages (output) for both power packs/ Are they the same? I can't see where there is a cause of difference between the 2 pin and 3 pin except that the 3 pin allows for a direct ground. If that is the case then the computer using the 2 pin connector is having issues with proper grounding which could be caused by power surges.

I would be more apt at believing that the problem lies within the output power differences between the two laptops....probably the one that uses the 2 pin is lowered powered than the one using the 3 pin....

2pin = 12volts
3 pin = 19 volts.

Without the models of the two laptops it is really too difficult to give a decent responce.