It is likely that you have a short on the circuit board. I ran into this issue before when DIY on a screen replacement. I had a company on ebay repaired for me afterwards. They told me that my circuit board was shorted when I asked. I must have slipped on the screwdriver a couple of times or forgot to unhook the battery. Anyway, they said a capacitor was burnt. I believe it was OCMobileplus on eBay.

It is possible to repair just the glass but I would rather leave it to the professionals. Would you rather spend $80 or $200 if you ended up breaking the LCD screen by doing it yourself? The chances are very high in breaking the LCD screen if you are a novice, because it is very difficult on this Nexus 6. I found a company on eBay that can do it for a very reasonable price: http://www.ebay.com/itm/Nexus-6-Motorola-Cracked-Broken-Glass-Screen-Repair-Service-/371722611096?ssPageName=STRK:MESE:IT

It is possible to replace just the front glass without the replacing the whole lcd screen unit. But it is very difficult. There are 101 ways to screw it up if you are a novice, and the whole LCD unit replacement will cost around $200. I would rather leave it to the professionals and save a lot of headaches. You can get it repaired for a very reasonable deal here: http://www.ebay.com/itm/Nexus-6-Motorola-Cracked-Broken-Glass-Screen-Repair-Service-/371722611096?ssPageName=STRK:MESE:IT

It will still work if the lcd screen is still displaying the image normally. Also, the touch digitizer is built in with this phone, and if either one is broken, you will need a whole new lcd replacement. You can get it repaired here: http://www.ebay.com/itm/LG-G5-Cracked-Broken-LCD-Screen-Repair-Service-/371844369196?hash=item5693a6cb2c:g:PVcA...

The glass only repair is difficult on this phone. The chance of you breaking the lcd is very high, especially, when you had never done it before. But you can get it professionally repaired here: http://www.ebay.com/itm/LG-G5-Cracked-Broken-Glass-Screen-Repair-Service-/371897989760?hash=item5696d8fa80:g:gVYA...