No, a USB to parallel printer adapter won't work. This month the SmoothStepper is set to be released, it will drive the steppers using a USB port and Mach3. I'm thinking of getting one myself.
There is also the Gecko G100, it's expensive though and not near as plug 'n play as the SmoothStepper.
Or you could shop eBay for a used laptop. Be warned though, some laptops won't work right with Mach3 even if they have a parallel port.