Before you try to remove the chip, check the cable - or perhaps you swapped the X and Y motor connections at the electronics end already, so you know the cable is OK. Also check the board for bad joints on the motor connector and on the driver chip pins.
Getting an old SMD chip off the board is easier in my experience than fitting the new one, because it doesn't matter if you overheat the old chip. The main thing to watch is that you do not lift any traces when the chip comes off. Use a small hot air blower of an appropriate size, make sure the solder is fully molten all the way round, and lift it off square. If you have an old hard disk drive lying around, practice on that.
Getting an old SMD chip off the board is easier in my experience than fitting the new one, because it doesn't matter if you overheat the old chip. The main thing to watch is that you do not lift any traces when the chip comes off. Use a small hot air blower of an appropriate size, make sure the solder is fully molten all the way round, and lift it off square. If you have an old hard disk drive lying around, practice on that.