The PS Vita does not turn on unless the battery is charged up to a certain minimum level. I've experienced it myself many times by letting my Vita drain completely and being unable to use it until after charging it for hours, this should be normal behavior for any PS Vita device.
On the other hand, it's weird that the Home button (aka. PS button) doesn't at least blink orange, which would indicate that it is charging. It's possible that the USB port you're using has a problem and is not charging your Vita sufficiently if at all. That's also something I experienced (once) in the past.
In my case, I was charging my PS Vita through the USB port of my Surface Book charger, but one day the Vita didn't charge at all. After opening my Surface Book, I was greeted by a message saying: "Your USB hub needs to be restarted" or something similar. Apparently, the hub "turned off" for whatever reason and stopped charging anything hooked to it (except for the Surface Book). My Surface Book managed to restart it successfully, and I haven't encountered any more problems since.
If you still can't turn on your Vita (10 hours at the time of writing should be more than enough), then try charging it elsewhere. Your USB hub might have encountered some problems.