|I looked up your battery on amazon (or at least one version of it).|
It looks like the kind that you install in a separate compartment unlike a netbook with an internal battery that you would disassemble the entire chassis to get at.
If you search "Lenmar Dell Inspiron 1420" you should see the battery I am talking about. That battery looks to have a built in charge indicator in the form of a five LED strip.
You will need to remove your new battery and check out the contacts inside the compartment then reseat the battery.
But, while you have it out, if your battery has the built in indicator I talked about, go ahead and press on that power symbol/button to check it. It will most likely say it is discharged since it was new, but if it happens to be otherwise that would be something to report. Most new batteries are not shipped fully charged and you have probably drained it further by now.
How did you purchase this new battery? Do you still have your old battery and can you compare the part numbers written on them?
If you can rule out a bad battery connection, incorrect battery, or defective battery, then it may be the charging circuit internal to the laptop.
message edited by ISAmad