Hi Leah,
I am sorry to hear that your installation is not completing properly for you on your new computer with Windows 8.1 and would like to help. I understand you have downloaded the driver from the HP website and are seeing the issue.
I would like to suggest:
Uninstalling the printer using this Removal Utility - LEVEL 3
Fully restart your PC
Reinstall the printer by using this HP Printer Install Wizard
I hope this helps!:)
Feel free to respond to let me know the outcome.