Hi,
In order for the kobo to be functional/restarted or detected when connected to computer, it needs to have sufficient battery power.
Try checking the charge port for fluff or debis and cleaning if necessary (look up how to on web) then check by using another charge cable.
Once you have confirmed that the device is charging leave it on charge for at least an hour.
If you cannot get the device to charge then you either have a depleted battery that won’t take charge or the charge port is faulty and needs replacement.
Hope this helps