I dont think this is a firmware problem, but updating firmware is a standard troubleshooting step so go for it. Printer firmware only controls what happens on the printer while you are describing a slowdown on your computer. The driver is mainly repsonsible for printer actions on a computer and should be where you are looking for solutions. Not sure what print driver you currentl have installed but HP offers several Universal Print Drivers on thier Drivers and Download page for your printer model. Try out one of the different varieties of UPD such as PCL5, PCL6 and PS to see if you can improve the situation.
If its not the driver then a core printing function on your Win7 machine may be having the issue. Most of the time when core printing is disrupted like the print spooler service it is often best to start with a reload of that machine and work your way back. Win7 also has a printing service called splWoW64 that is known to hang jobs. Sometimes all you need to do is find the splWow64 process running in your task manager and manually shut it down to get the print jobs moving again, although its only a temporary fix.
Anyways, good luck and keep us posted if you discover more information.