Now this is odd! When you click on "More Info", you should get a column called "Contents" on the left. In this column you should see a heading called "Hardware". If you click on the flippy triangle to the left of "Hardware", you should get a list of stuff, and "Power" should be on this list in alphabetical order--probably just above "Printers". If you click on that, you should get information on your System Power Settings. If "Power" is truly missing and not just hiding, please post back. If you do get to "Power", you should be able to see a heading called "Battery Information". If you do, what does it say? If you don't, please post back that you don't see it.
As to the power adaptor, it's possible that it could have a problem. However, the real problem seems to be that the computer will not run off of the battery alone. If the computer will run off of the power adaptor alone, then that would indicate that it is probably working well enough. When you say it is a little bent, do you mean the pin?
What is the history here? Was there any problem with the previous battery not charging? Or running off of the previous battery before it died?
One thing I am wondering--could the new battery not be the right one for this iBook? Did you get it from Apple or elsewhere? If elsewhere, what is it and where did you get it?
Do you happen to have access to an Apple Store or a friend with an iBook? If so, you could try another power adaptor and see if that helps. If a friend has an iBook with the same battery, you could try swapping batteries and see what happens. It is possible that you got a defective battery, and if you did, you should be able to exchange it for a new one. I am inclined to think the problem lies with the battery rather than with the power adaptor at this point, although it's possible there could be a problem with the DC In Board.
Please post back on whether "Power" is truly missing and a little more information on your new battery. Maybe also what happened to make you decide on a new battery.