Extending battery life

Based on the symptoms I would suspect a failed lithium battery. Most people think they should keep their lithium batteries at 100% but that actually shortens the life (number or recharges). I always suggest that you should try and let your laptop run down to 50% before recharging. Leaving a laptop constantly plugged in results in the same outcome - constant recharging of small amounts so you can see that the 'life cycle' is related to the number of times you recharge and if you are constantly doing it then you will most likely be shortening the battery's useful life. Unfortunatley most laptops will not run without the battery so the user's only option is to run their laptops on battery and not plugged in to AC until at least 50% dissapation thus optimizing the battery.
Just in case you have not done this, try removing and reseating the battery. Jarring of the laptop can somtines alter a good connection but from what you said it is unlikely.

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>

A Class 6 memory card is required for recording HD quality video. Not sure if yours is HD or not. Anything lower than Class 6 (such as Class 4 or Class 2) will result in recording issues and possibly skipping some video here & there.

As for the 30 seconds of filming limit...

1) It may be the memory card...that is if it's lower than Class 6. As a rule of thumb, when it doubt, buy Class 6 or better. Class 10 is the next step up, but it's a quite a bit more expensive.

2) Make sure you are using good, Lithium batteries...not Alkaline. Alkaline batteries will shut the camera down after a very short period.

Here are more tips on shortened recordings from GoPro's Website, followed by their Support Contact Info:

The batteries do not last very long.

• It is not recommended that you use Alkaline batteries. Lithium batteries have the best results and longest battery life. Rechargeable NiMH are another option in mild weather.
• Is it cold out? Battery life can definitely be affected by the cold! Please make sure you only use Energizer Lithium batteries in the cold, as any other battery type will perform poorly. In cold temps, you can expect about half of the normal run time when using the Energizer Lithium batteries.
• Still having shortened records with a good set of the recommended batteries? Please email our support team through http://gopro.com/support for further assistance.

http://www.gopro.com/support