Hello, TheLoneCrusader can you answer a few of my questions so I can better understand your issue, from there I can should be able to help you.
What OS is currently on the laptop?
Also do other devices connected to the same network currently have internet access?
What browsers are installed on the laptop?
If the OS installed is Windows, is the OS up to date?
For now you can some of these steps. Firstly try accessing the internet from a fresh browser install, try uninstalling google chrome if you have it already and install google chrome. If that works then your browser is possibly failing in some way, you can fix that be reinstalling that browser. If that doesn't work continue to the next steps.
As for the information you've given me, you can try resetting your modem, and router and see if this resolves your issue.
You said that you can connect to your network and you can see the signal strength is good, that being said I'm assuming the wireless receiver in the laptop should be functioning.
Try these steps (assuming your on windows)
Go to control panel, then network and sharing center, then change adapter settings.
Look for the wireless adapter, then right click it, then click disable, after it's disabled re-enable it.
Connect to the network again and check for internet access on a couple browsers
If that doesn't work try what Laptop_Nerd suggested by uninstalling the Wifi adapter, if it doesn't automatically reinstall the driver, lookup your computer online and find the driver from your specifics computers support/driver page.
Then try accessing the internet on a few browsers.
If all that doesn't work let us know.