Phone won't turn on

Hi so I replaced the screen on my Nexus 5 and now it won't turn on.

I put everything back into my old screen and now that one wont turn on either.

When I hold down the power button nothing happens .

When I plug it in the screen turns on, and the battery charging symbol comes on, then it shows a battery charging up.

Then the screen turns off and that's it, nothing happens. No red charging light. When I try to turn it on nothing happens.

When I plug it into the PC my PC makes a noise like a USB device is plugged in, but when I go to "my computer" The phone doesn't show up. The screen lights up, like it's charging, then the battery shows up that it's charging, but then it turns off and nothing happens.