For the Y axis stepper motor, try swapping out the cable to it with the X stepper cable and see if it works, that would isolate the cable or the MightyBoard. If it still does not work, contact sales for a replacement.
With ReplicatorG, once you launch the app, connect the printer, then select the menu "Machine->Connection (Serial Port)->Rescan serial ports". Then, go back to "Machine->Connection (Serial Port) and there should be an entry for "/dev/tty.usbmodemXXXX" with the XXXX being some number.
Lastly, "Network unavailable or update site timed out.": in the "ReplicatorG->Preferences", select the "Advanced" tab. Firmware update URL is set by default to "http://firmware.makerbot.com/firmware.xml" I don't know for certain, but I'm pretty sure Makerbot doesn't host firmware for the MBot Cube Kit. The official link for firmware from MBot is http://firmware.mbot3d.cn/firmware.xml according to http://www.mbot3d.com/software. Try putting that xml address into ReplicatorG's preferences, but you will likely get the same "timed out" error. The current firmware version is 7.7, so as long as you have that, the error can be ignored.
Hope this helps.