I have said board Adruino UNO/CNC shield combo. Can't get it to work with Mach3. Isn't that possible? Does Mach ONLY work with parallel port?

As far as i know Mach3 and the Adruino UNO/CNC shield combo will not work together.

There is a Mach3 board that uses a USB port, look on Alibaba.com

If you want USB support for MACH3, you will need a usb controller.. The most common ones I have seen are the UC100, UC400 boards.. You can also use a Ethernet smoothstepper which connects to your machine over cat5 through the Ethernet port..

Any device other than the parallel port requires a plugin to allow it to communicate with Mach3. I don't know of any plugins for Arduinos.

I have said board Adruino UNO/CNC shield combo.

You would ask the suppliers of the Board/Shield combo as it would be their responsibility to create and support a plugin to support their hardware,

 - Nick

This was sort of answered in another thread.  If the shield board has enough power for the motors you are using and has the stepper driver chips to handle it, the board can be directly wired to a parallel port connector, or better, a parallel port breakaout board.  Most of shield boards follow the open source spec, so the connection points are clearly marked.  You'll probably want to go with some connectors(look for dupont connector sets) to attach to the board.  If this is for a mill or other heavy load I would get at least DRV8835 stepper chips(up to 36 volts) and at least a 24 volt power supply with enough amps to run all the motors full speed at once.