OK, thanks for the additional information. I understand it is supposed to be plug-and-play, but it was manufactured to be compatible with Mac OS 9.2 and OS X 10.2-10.6, which are now five major OS X revisions old or more. Sometimes older peripherals simply aren't supported by the manufacturer past a certain point.
If Dell Support couldn't get it to work, then we probably couldn't add anything further to the troubleshooting effort. You could try another USB cable, in case the one you are currently using has failed. Also, you can check in > About This Mac > System Report... > Hardware > USB to see of the printer is even recognized as being connected to the Mac via the USB cable.
Well, I don't know what's happened here, but I disconnected the printer, started again and it's working. Thanks for your suggestions. I thought it was going to be a new printer.