Lenovo T400 power

[Bimmertwo]

Can I use the laptop with just the power adapter and no battery? I was told its ok but mine is not working with only the power adapter and when battery is in I get message that it's plugged in but not charging. What to do?
Updated info:
Laptop is Lenovo ThinkPad T400
OS is Windows 7
Adapter Driver: Microsoft 6.1.7600.16385
I bought it used so have no history of system updates or restoration attempts

 

[Titillating]

It's possible you have a faulty power adapter. Any chance you can get another adapter to test if it will work?

 

[JeckeL]

Is there a link-light or status-light type of LED right near where you plug the AC adapter in? Does it light up when you have the AC adapter connected?