Hi Dan K,
Welcome to the HP Forums!
I would like to take a moment and thank you for using the forum, it is a great place to find answers. For you to have the best experience in the HP forum, I would like to direct your attention to the HP Forums Guide First Time Here? Learn How to Post and More.
I see that your Mini start and load the Windows logo but then hangs or locks up. Here is a document to assist you with that. Computer Does not Start (Windows 7, Vista, XP)
If you would like additional assistance, please respond with the exact model of Hp Mini you have and the Operating System you are running. How Do I Find My Model Number or Product Number?