Laptop connection issues

If the HP laptop connects to your wifi and shows a good signal strength, then the laptop should be getting a valid private IP address from your router, something like 192.168.1.x. However your router should then be seeing the HP under its connected devices list. Given its not, then it sounds like a corrupt setting on the HP for the network configuration and it cannot establish an IP connection after its established the radio link too your wifi.

I had similar issues with an HP laptop and resolved it by resetting the network drivers and doing a full hard reset of the laptop. Incidentally, the hard wired ethernet connection worked fine on my laptop and it was just the wifi that couldn't reach the internet despite connecting to my router. So it was the network settings specific to the wifi module in the HP.

Here's HP's troubleshooting guide to follow: 

https://support.hp.com/nz-en/document/c02543015