Nexus 5 won't boot into OS, bootloader/adb won't let me do anything either Nexus 5 power button started "sticking" and would get itself into a "boot-loop". I looked it up and it seemed lots of users were having issues with the power button on the Nexus 5, so I just decided to live with it (I could un-stick it if I fiddled with it enough). 
Cue two weeks later and the power button is getting stuck more often and also getting harder to unstick, oh and the phone won't boot into the OS anymore (It just sits permanently on the Google loading screen). Took it to a repair shop and they told me it wasn't hardware related. 
Now I have two problems, power button is still a pain in the ass, but not being able to boot into the OS is even worse. Could it be software related?
Try "Wipe data/factory reset" and also "Wipe cache partition". Doesn't work. Keep getting E: failed to mount /cache errors 
Install ADB and Fastboot. Try running adb devices (no device), then I select "Apply update from ADB" on my phone and then try "adb devices" and the device is recognized (as "sideload"). I try running adb sideload ROM.zip and I get "error:closed". The phone logs:

Now send the package you want to apply
to the device with "adb sideload &lt;filename&gt;"...
E: failed to mount /cache (Invalid Argument)
E: failed to mount /cache
E: failed to set up expected mounts for install; aborting
Installation aborted.



If I try to run any adb command on my phone I keep getting the same errors (error: closed and E: failed to mount /cache)

Any ideas of where to go from here?
I was pretty much having the same problem. 
I was told that my partitions might be messed up. 
Unfortunately I won't be able to test out a fix for it until I get home from work today. But definitely look into corrupt partitions. 

Infinite boot animation screen Nexus 5