That might be related to a known problem with the last firmware released to the Kobo. It is discussed in detail in
Kobo E_Reader wifi upgrade gone bad. I don't think I have seen a report that this prevented the PC from seeing the device, so it might be something else. The solution seems to be restoring an image to the internal card. And as it is not responding now, the image is probably the way to start. I have sent a PM with a link to the image.