HP Solution Center cannot run "because your device installation is not complete"

I have Windows 8.1 and a Photosmart B110a ‘all-in-one’ printer. I was unable to scan because HP Solution centre said the unit was “disconnected”, despite it being connected (by USB and wirelessly) and printing perfectly!

I did a full re-install (after downloading from HP - I can't find the software CD) but then when trying to launch HP Solution Center it said: "HP Solution Center cannot run because your device installation is not complete. Please plug in the USB cable or re-run the setup programme from the installation CD for a network installation. (etc.)"

I’ve spent three hours trying unsuccessfully to solve it: I’ve used HP Print and Scan Doctor, reinstalled the HP software three times, checked for Windows updates, removed and added the printer (it appears twice, as a USB and wireless connection) and successfully done document scans from within the test software.

I still get the "HP Solution Center cannot run…” message.

Can anyone help please?