Laptop/Notebook power issue....Need help.

[kmondrush]

I have a old NEC versa 4050H laptop. Recently I have problem with the computer when charging the battery. I would plug the AC charger in and the battery would start to charge. Sometimes the computer would slowly charge then jump to 100%. After unplugging it will run for a few minutes then shutdown. I thought it was the battery, so I purchase another one. Because of the age and value, I went for the used pull instead of brand new. Same problem with the other battery. I have also replaced the cmos battery (brand new). Last thing to replace is the bridge battery. Does anyone have any suggestion.
Second thing is if it is possible to run the pc without a battery installed.
I was thinking that the battery circuits could be flaking out. I’m not sure if the bridge battery would allow running of the laptop without the battery or if it is just to provide juice to the memory during a battery swap. Since the bridge battery is bad, I haven't been able to test it yet. As it is now, it will not run without a battery in the battery compartment.

[EzyStvy]

I have an older Sony that won't run without a "working" battery. Newer lappies don't have this problem.