The HP-installed software (remember I said "old") would keep the Windows XP and 7 loading systems completely hamstrung for many minutes.
With the printer connected and on the system would be up and ready to roll within a few minutes. Off/disconnected and it was always 30-35 minutes. Connecting and switching on the printer once the wait had started had no effect.
On my current machine, Win 8 >> 8.1 this effect is absent. Booting is always fairly quick - with the identical printer drivers installed.
Amusingly, the printer involved, an HP PSC 1610 All-in-One died on me last week. Over the weekend I completely removed the 1610 from each of those three systems before setting up the new one. (Printers screen/Uninstall all drivers and related programs/thorough cleanup of directories).
The XP and Win 7 machines now magically boot in 2-3 minutes independent of the printer.
Installed the drivers for the replacement HP Envy 4500 and it made no difference to the boot times.
One happy bunny.