Have you double checked the obvious and tried a different USB port and different USB cable?
Is your 3in1 printer a network compatible unit? If so, you may have installed the wrong device driver for USB use.
Have you tried looking for a newer driver from the printer manufacturer's website? There's a good chance you'll need a newer driver than what came on the disc with the printer if your new computer is running OSX 10.6, "Snow Leopard."