The install on your current computer is corrupted. Uninstall and reinstall the software from Programs and Features and try again. Make sure you are using the latest version available from HP's support website.
If that does not work then find an alternative Print Driver such as the Universal Post Script driver for Win7x64 and install the printer object with that instead.
In regards to the firmware update you can always borrow another computer. Try installing it on another machine then run the firmware update. It would be best to find a WinXP or different OS instead of another Win7 machine if possible.