Hello Floppinfrog, and welcome to the HP Forums. I hope you enjoy your experience!
I you are having problems with your print queue. I would love to help you, but first if you could post your product number for your printer, and include what type of printer it is. I am linking an HP Support document below that will show you how to find your product number. Also, please include which operating system you are using. Also, if you're using Windows, please include whether your operating system is 32-bit or 64-bit. With this information and the product number I can provide you with accurate information.
How Do I Find My Model Number or Product Number?
Mac OS X: How Do I Find Which Mac OS X Version Is on My Computer?
Which Windows operating system am I running?
Is the Windows Version on My Computer 32-bit or 64-bit?
As well, please include the connectivity information of your printer to computer setup. Is it connect via USB cable or via wireless?
Please let me know when you have gathered this information and I'll do my best to assist you! Thank you for posting on the HP Forums!