I am sorry that you are having continual trouble with your installation. I am glad that you are coming for a private workshop in two weeks, as it will open up so much to you. I look forward to meeting you.
When you say that there is "nothing in the LLK slot", does that mean that there is no cartridge in the cartridge slot. Do you mean that type of slot?
That there is no Gloss Overprint being printed on a glossy paper nozzle check through the LLK channel?
If the latter, as Dana explained, GO is nearly perfectly clear so that you can only see light reflecting off it at an angle and only on glossy inkjet paper. So if you are certain that there is nothing coming out of the LLK ink channel from the print head - then...
... if an ink is not printing out of an ink channel that recently was able to print ink from that ink channel, then it can only be for a few reasons. Let's rule out blown printhead controller board, bad pump manifold, loose air line to that position, broken off air stem, defective cartridge. In any of these - there is nothing you can do right now to remedy that.
1) The cartridge was not primed correctly or it lost its prime before installing. Re-prime the cartridge and perform 3 POWER CLEANS - not regular cleans, but POWER CLEANS to purge the air safely from that ink channel.
You can see how to prime the cartridge correctly here at about the 4'30" mark: 3800 / 3880 Cartridge Instructions Video Make sure you check the exit chambers for prime.
2) If the printer was not previously used for a long period of time (and therefore ink was not printing recently from the missing ink channel), and then the printer is installed with inks and POWER CLEANS or INITIAL FILLS are run, it is possible that very old pigment was picked up off the ink lines and deposited in and clogging the ink filter of the damper in the ink exchanger. Replace the ink exchanger or use PiezoFlush to try and resolubize the old pigment and remove it from the damper through the print head. This requires an INITIAL FILL, followed by 48 hour rest, then followed with an INITIAL FILL.
I recommend starting with 1) re-priming your GO cart. Running the POWER CLEANs (not regular cleans). Try for the nozzle check and hope it is just air in the ink lines from an incomplete or failed priming.
If that is not successful let us know and we will send a new cart for you to transfer the GO to. These carts rarely rarely rarely every fail. So I think that the prime and purge may do it.
Let us know how you get on with 1). It may be very obvious that the exit chambers are not filled.