So, regarding my cry for help...

I did get several replies and did more research on my own. The TL;DR up to now is "I have a fully functioning device with no input method and my data may well die on it":

  • The device is passphrase-protected and encrypted so I can't simply connect an USB cable and use MTP.
  • I can't connect a mouse or keyboard as LG, in their endless wisdom, didn't design the USB port with enough power in mind so it can't support USB OTG on its own.
  • Google then removed USB OTG support from the Nexus 4's kernel. It's not as if powered USB hubs existed so this is obviously the correct path of action.
  • While I can install new programs via Google Play, Android 4.0 and above prevents newly installed programs to start without user interaction.
  • LG points towards a third-party service for out-of-warranty repairs and as part of their Terms of Service, you have to forfeit all data as they "always update the software", i.e. they will prolly ship random other devices to you on a regular basis instead of what you sent in.
  • The Nexus 4 is running stock Android, locked bootloader and all

The last two options I see are

  • Try to find a way to get a custom ROM onto the device with the help of USB cable and physical buttons only without destroying the encrypted data (yeah, right...)
  • Try and source a display so I can repair the device myself. But as not even ifixit.com offers a howto or parts... I suspect this may fail.

And I can not even be reached under my normal number as I don't dare turning the device off and/or removing the SIM as that may prevent me from recovering with the running device, somehow.

Another option is that you buy another Nexus 4 and switch the mainboard. You still need to open the phone, and even two phones, risk breaking both of them. But at least the display part is probably more intact. You could also use a second-hand Nexus 4, just as long as the display is not broken, or if you have a really good friend with Nexus 4, ask him to loan his phone for the operation..
Comment by suuri 2013-06-18--08-50-18-CEST
I am not sure where the actual data is stored and/or if there are no security features that will eat my data as soon as they detect changes, though...
Comment by Richard 2013-06-18--09-08-58-CEST
WRT not being able to start an app on install -- what you can do, however, is have an app registered as a broadcast receiver for intents like power status change, or start them on boot. Could be a way to get an app to start...
Comment by cm+google 2013-06-18--12-13-38-CEST

If the Nexus 4 does not diverge from the implementation described under http://source.android.com/tech/encryption/android_crypto_implementation.html recovering the data should be easy, IF you get to the raw partition data...

The problem is this: Unlocking the bootloader (which needs to be confirmed on the screen) wipes the phone. So you need another way to get there. Since the Nexus 4 uses eMMC, it might be possible to connect a debugging tool (Bus Pirate, JTAG dongle) directly to the eMMC and dump its content... I don't see any other way currently... :(

Comment by 23.gs 2013-06-18--16-46-34-CEST
Regarding the SIM card: you can request a replacement from your provider and leave the old one in the phone.
Comment by cstamas [openid.ppke.hu] 2013-06-19--09-02-27-CEST

Googling led me to this video which shows how to replace the screen, with links to the parts needed in the description.

It does involve pulling the battery out, so I'm not sure how that would affect encrypted data.

Comment by Beojan 2013-06-21--12-21-37-CEST