Don't throw the old one away just yet - it may still work and will come in handy for this trial. Put the old one back in and power up using it if it wlil work for about three minutes, or use the electric main. Go into Control Panel>System>Hardware (if XP) >Device Manager and right click the entry marked Battery. Uninstall both the Microsoft battery related entries and turn off the computer. Pop in the new battery and start up without main electric spport. If it doesn't work, plug into the main and try again.
I have a Samsung with the same problem and the above didn't work for me but it's worth a shot. The Samsung battery has its own lights showing it's four fifths charged but only lasts a minute in the box before shutdown so it must be a motherboard problem. Hopefully, your's is not that bad.