Arduino board not detected when connected via USB
Going by the description, the FTDI drivers on your other laptop have either gotten corrupted, been replaced by an invalid version, or are blocked due to lack of digital signature. Clearly, since the InduinoX still works as expected on one laptop, the problem isn't in the board. 

Steps to diagnose / resolve: 


Disconnect all Arduino boards from the other laptop, then manually remove any FTDI drivers that may be installed (they won't be active so won't show up in device manager). You may need to use the CDM uninstaller (download from FDTI site).
Download and install the latest FDTI drivers from the FTDI web site, by running the setup executable. Ensure you download the appropriate version of the drivers, Windows 7 32 bit or 64 bit as appropriate
Restart your computer just to be sure.
Connect the InduinoX back to the USB port, then see if the drivers configure themselves fine. 
If the computer still doesn't show an additional COM port after this process, check for any devices in Windows Device Manager, with a red error flag. Right click and reinstall the relevant drivers, manually selecting the source folder as either the FTDI folder if you downloaded the ZIP file, or by unzipping the FTDI driver ZIP file that comes with the Arduino software distribution.
Once the new COM port shows up in device manager, fire up the Arduino IDE, and make sure you select the right COM port and the right board type ("Arduino Uno" works for my InduinoX board)


If it still doesn't work, you may need to reflash the bootloader on the board, but that is a very unlikely solution.



Post-script: Also see the InduinoX installation page.