Re: Sanguino 1.3b Power Connector Question.

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Would I just need to de-solder the screw terminal and solder a Molex or ATX connector in its place?

Yes.

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Also is it just one or the other or do I need both the Molex and ATX connectors?

That depends on your configuration:
From Sanguinololu#Features:

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Supports multiple power configurations:
-- Logic & Motors supplied by ATX power supply (needs molex harddrive connector, and optional 4pin atx connector for additional 12v/supply voltage)
-- Motors supplied by 5mm screw terminal 7-35V
-- Logic supplied by USB bus
-- Logic supplied by optional on-board voltage regulator (molex harddrive connector cannot be installed at the same time)

If the board gets 5V from usb or a voltage regulator, you don't need the molex.
The hotbed needs a lot of current (~10A), if you are working on the board you might aswell look into the heated bed current problem, if you intend to use a heated bed with the board: Sanguinololu#Bugs overheating mosfet

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is it true that you can communicate with the board with just the A-B USB cable connected?

With just usb connected you should be able to communicate. Is the ftdi driver installed and did the com port show up on your PC? What errors did you get?