Macbook Pro (late 2011 15") is stuck in a boot loop It boots up until the progress bar is at about 80%, then it flashes to an empty grey screen, no login window shown, no Apple logo. 30 seconds later it reboots on its own. 

Things I tried:


reset the PRAM/NVRAM
reset SMC 
booted with d+shift: no indication of any kind of different boot, same as normal boot
booted with cmd+r: it doesn't boot to the recovery window, but switches to "Internet Recovery". Internet Recovery runs to 100% before switching to the grey screen
ran Apple Hardware Test (quick and extended): no failures
tried to boot from an "Install Sierra" USB pendrive: it recognizes the pendrive, but boots with the same behavior as a normal boot
booted to single user mode: I can boot to Single User mode and run fsck on the different partitions. I cannot repair user permissions (thanks, Apple, for removing that functionality). 
booted with a live Linux USB-stick: it works, although I have to enter the boot option "nodmraid". However, I cannot start Xorg. I can ssh into the MacBook when booting with Linux. I also ran testdisk and recovered (at least I think so) the partition table. Both, the normal Mac partition, as well as the Recovery Partition are there. 
booting to verbose mode. 


Some errors occur:

task_exceeded_footprint: failed to warn the current task...




AppleKeyStore: operation failed (pid: 45 sel: 7 ret: e00002c2....




configureInterests - nElements &lt;= 0!Failed to configure interests
I080211Controller:addSubscriptionForThisReporterFetchedOnTimer() Failed to addSubcription 

I080211InterfaceMonitor::configureSubscriptions() failed to add subscription


and it finally stops at

IOConsoleusers: gIOScreenLockState 3, hs 0, bs 0, now 0, sm 0x0


Any help is appreciated. Does this mean it has a dead GPU? I just found out that Apple's repair program ended in December 2016...
Does this mean it has a dead GPU?

Yes. Absolutely. This means it is one of thousands GPUs killed by inadequate thermal design that finally bit the bullet. As all MBPs from that era are defective by design it is impossible to keep them around for the amount of time you would expect from a quality product.
If this machine is still around then it can be partially resurrected with a procedure like this:
https://apple.stackexchange.com/a/295805/251859
This bypasses the AMD GPU through a forced EFI variable. No amount of SMC reset voodoo or the like will restore a GPU dead MBP.
You might want to bake the chip for a flaky temporary fix like with the iBake procedure.
The only real fix though is to either sue Apple like they deserve for lying on this to us all or to replace only the AMD chip in question. That is way cheaper than to go the now defunct Apple road of replacing a faulty board with another faulty board.
Converting it over into a Linux machine makes the GPU bypass on a defective machine easier, but will not do much good for keeping it around long enough.