Sounds like this is the WiFi key -- which some folks mistakenly call the Internet key. But regardless, you should not be having the PC shut down when you press this key.
To determine the cause with hardware failures, you have to be able run diagnostics. We have no way of accessing your PC from here, so we can not do that for you. You have to do it yourself.
You do this by pressing the Esc key repeatedly when rebooting and then, when the HP Startup Menu appears, selecting Diagnostics (usually F2) and letting it run.
If it is NOT possible to run diagnostics, or if that does not work, then there is NOTHING more you can do by yourself -- and there is NOTHING we can do because we have no way of accessing your PC from here to run diagnostics or repair hardware.
You will need to have the PC physically examined in a service facility by folks that can run their own diagnostics to determine what is wrong with it.
-------------------- If your PC is still under the original one-year HP warranty, or if you have purchased an extended warranty from HP and this is still valid, then having HP do this is an inexpensive option for you. In that case, you should contact HP Customer Support to see about having it repaired or replaced under warranty.
Here is how you can get in touch with support: Step 1. Here is the link: http://www.hp.com/contacthp/ Step 2. Select the product type. Step 3. Enter the serial number of your device or select let HP detect your product option. Step 4. Select the country from the drop-down. Step 5. You should see the HP phone support number or Chat option listed.
-------------------- If your PC is no longer under warranty, then it will cost you up front to have HP examine your PC. If you want to do that, you will have to contact an HP Repair or Service Center to see if they can examine the PC to determine the cause(s) of the problems, if it can be repaired, and an estimate of the repair costs.
Be alert for scammers posting fake support phone numbers and/or email addresses on the community. If you think you have received a fake HP Support message, please report it to us by clicking on "Flag Post".