Hello and welcome to the forum.
Other jobs hang in the queue forever.
I had this problem once and believe it or not I had the wrong IP address for the printer port and the job was actually going to another printer on another floor in the building.
Test pages go to queue and disappear but do not print.
It never produces an error at all??
Is there anything unique about this particular computer? Does it have a security suite that is not present on other computers? Does it have any other software packages like LogMeIn, Citrix, some type of network manager that the other computers do not have?
Does the printer have a static IP address? If not then perhaps you might want to set that up.
My suggestion would be to create a new standard IP port on the computer (using a the manually assigned, static IP address of the printer(s), making sure that there are no conflicts with other IP addresses on the subnet).
IF the computer is not having any problem installing drivers or printing to USB printers when attached, then there is not likely any problem with the print process or spooler service on the computer and it's down to the network or some third party rogue software, process or service that is likely causing the problem.
You might want to try a clean boot of the system
https://support.microsoft.com/en-us/kb/929135 just to see if it might be associated with third party products.
Good luck and keep us posted.