Laptop Problems

I have an HP Pavilion dv5 laptop computer that connects to the internet through a wireless router.
I am able to use the internet just fine when the laptop is plugged in, but when it’s unplugged (i.e. running on battery power), the internet connection slows down to a degree that it’s virtually non-existent, and I keep getting the infamous “Internet Explorer cannot display the webpage” page.
When it’s plugged back in, it works flawlessly again.
I have tried to diagnose the problem, and even went as far as reinstalling numerous drivers and Flash BIOS at the direction of HP’s Online Support, but the problem still exists.
Can anyone help me?