There are no free keys for Windows 7 that I know about.
Most user don't need the few extra expensive features in Pro version so I'd check to be sure before having your work buy you one: Compare Windows 7 Editions - Windows 7 Forums
Your options since the Home Premium Product key is faded are to go ahead and do the Clean Reinstall then call MS phone activation option to ask them for help with the faded key. We have multiple reports that they will ask for other information on the sticker and then replace the key.
If this fails after trying several different agents if necessary then order your Factory Recovery disks from HP tech support which activate themselves. These disks were supposed to be made when you set up your PC.
You can also research how to back up the existing SLP factory activation file to reinstall it after a Clean Reinstall, however the Administrators have decided this operation is not supported here due to the possibility of abuse so we cannot help further with it.