I thought about this some more and realized that there are at least a couple cases where the green LED could be off while the Wixel is being supplied power by a computer. (The green LED actually requires an action from the microcontroller on the Wixel in order to be lit.) Since your Wixel’s red and yellow LEDs are lit, it seems like the device is getting USB power.
One of those cases is when the Wixel is already in bootloader mode, which I suspect to be true for your Wixel. It is also sounding like your Wixel’s USB bus is in suspend mode, which can happen if USB communication was disrupted by damage to the board or damage to the cable.
Can you verify that the new cable you purchased works for recognizing other USB devices? If the cable does not work when connecting another USB device, you might try using other USB ports or maybe even another computer.
Also, many of our customers use Wixels in pairs. Do you have another Wixel? If so, are you able to get it to be recognized by your computer with the same USB cable you are currently working with? Also, did you purchase your Wixel(s) directly from us?