Cannot connect printer to MacBook Air

I just got my neighbor to replace her aging Windows PC with a new MacBook Air, and while I was setting it up for her, the only problem I ran into was with the printer. It is a HP LaserjetPro connected via USB (no wireless available). The Mac sees the printer, and I can send something to the printer, the print monitor acts as if it is printing, but nothing happens at the printer. When I download the HP Software, it cannot find the printer.

So far, I've tried re-booting the MacBook and Printer, disconnecting and reconnecting the USB cable, and resetting the print system and re-adding the printer several times. I don't know what else to do, and they're going to have to return the MacBook and buy another Windows PC if I cannot fix this.

Any ideas?