What is on the screen now, and what happens when you try to turn it on? Does the power LED do anything.
The things to try are:
- Charge the device and try to turn it on.
- Force a power off by holding the power switch in the off position for 20 seconds and turning on.
- Factory reset using the instructions on https://wiki.mobileread.com/wiki/Kobo_Reset:_Aura_H2O
- Restore an image to the internal SD card. For the Aura H2O, this is the last resort as it breaks the waterproofing.
Also, "can't connect to computer" is expected. The Kobo devices don't automatically connect, so if one is detected by the computer, then it is probably a bad sign.