The laptop does not charge the battery but the battery charges off the laptop (long life battery)

Eventually your battery will have a short/no life indeed. Though this happens to all laptops.
Using your laptop while it is charging isn't going to damage anything. It just means that the battery will take longer to charge because you're using the laptop.
To get the most life out of the battery, fully charge it and then use it until it is empty. It's also a good idea to remove the battery when the laptop is connected to the mains supply.
All you're trying to do is extend the life of the battery. The day will come when it holds a short/no charge.

Step 1:
No just the laptop charger needs to be plugged in.

Frequent Charging Shortens Battery Life Frequent charging shortens the life span of a Lithium ion battery. Batteries should be charged only after they expend all their power. b> Switching Batteries Switching batteries helps preserve battery life: If a cell phone or computer user puts in a spare battery while separately charging the primary Lithium ion battery, that helps extend the life of both batteries. b> Removing Batteries Most laptops charge the battery when a user plugs in the AC adapter. Users can adjust this setting by changing the power options. Windows places this option in the Control Panel, while the Gnome Linux desktop places power options under "Administrative Tools". Cell phones incorporate their own power-saving features that the user usually cannot control. b> When to Replace a Lithium Ion Battery If a laptop battery does not hold a charge for more than a few minutes, a user must replace the Lithium ion battery if he wants to use the computer without an AC adapter. b> Other Ways to Extend Battery Life Storing a battery in a cool, dry environment causes a lithium-ion battery to last a little longer and reduces the frequency of needed battery replacements. Battery Bar - Free version available
http://osirisdevelopment.com/BatteryBar/index.html

Problems with power usage and battery life - Mr Fixit
http://support.microsoft.com/gp/windows_battery_power_settings

How old is the battery ? it might be past its use by date
Batteries can only be charged a certain amount of times before they need to be replaced

Frequent Charging Shortens Battery Life Frequent charging shortens the life span of a Lithium ion battery. Batteries should be charged only after they expend all their power. b> Switching Batteries Switching batteries helps preserve battery life: If a cell phone or computer user puts in a spare battery while separately charging the primary Lithium ion battery, that helps extend the life of both batteries. b> Removing Batteries Most laptops charge the battery when a user plugs in the AC adapter. Users can adjust this setting by changing the power options. Windows places this option in the Control Panel, while the Gnome Linux desktop places power options under "Administrative Tools". Cell phones incorporate their own power-saving features that the user usually cannot control. b> When to Replace a Lithium Ion Battery If a laptop battery does not hold a charge for more than a few minutes, a user must replace the Lithium ion battery if he wants to use the computer without an AC adapter. b> Other Ways to Extend Battery Life Storing a battery in a cool, dry environment causes a lithium-ion battery to last a little longer and reduces the frequency of needed battery replacements. Battery Bar - Free version available
http://osirisdevelopment.com/BatteryBar/index.html

Problems with power usage and battery life - Mr Fixit
http://support.microsoft.com/gp/windows_battery_power_settings b>

2 hours is enough for a battery to be completely charged...

Once the battery is charged you can remove the power supply and use the laptop till the battery drains up to 10% to 14%......
This will increase the life time of battery... If you keep on charging the battery continuously when using your laptop, then the battery life will be shortened very soon...
So charge and drain the battery properly... This will increase the life time of battery...

Thanks for the info mate. Also to mention that some HP laptops have air vents at bottom, so they cant be placed on bed or even lap for a long time. This causes overheating, and again reduces the battery life.

Would be useful for many people

Will the old battery (that you are replacing) charge up at all? If the old battery charges but the new battery will not, then it's likely a bad replacement battery.

To rule out the possibility of a corrupted battery meter inside of windows, you may wish to leave the laptop on battery power only, until it dies. A 5% charge will usually only grant you about 20 minutes of laptop life maximum. Since you left it charging all night, you should get a few hours of life before it dies. If you get a few hours of life, the battery meter software is corrupted.

Most likely though, the replacement battery is bad.

usually 8 hours.

for first charge.

on a brand new battery