Thorwall
Hello;
Allow me to welcome you to the HP forums!
Sorry for the bad news but HP only warranties their PC for use with the original OS that comes preinstalled on the PC.
If you replace that with something different, or add a different OS, HP does not provide support for that.
In addition, HP does not supply Linux drivers -- so for these, you are on your own.
In your case, I would suggest you post on the Linux Mint Forums -- where there are folks experienced with dealing with Linux driver issues: http://forums.linuxmint.com/index.php?sid=e1d864fe510e562a3fca15f38c93b95a
Good Luck
I am a volunteer and I do not work for, nor represent, HP