1
Your description of the problem indicates most likely there is a problem with the battery, did you purchase that new battery direct from the laptop manufacturer or is it not an OEM battery purchased from a 3rd party retailer?
Also, what is the make and exact model number of your laptop.
2
In the meantime:
Open Device Manager (accessible by right clicking your Start Button)
Expand the Batteries section
For each device in that section:
Right click and choose Disable
Wait a second or two, then right click and choose Enable
Close Device Manager
Then, restart (not shut down) your laptop and check if the battery is charging correctly.