I am going to assuem that the 9845A printer is very similar to the one used in the 9845B. I have some knowledge of the latter machine.
The printhead/mechanism is used in another HP product (at least) -- the HP9876A thermal printer. But I suspect those are as rare as 9845s now.
Anyway, the printhead is actually quite complicated. It consists of a 560 bit shift register driving the 560 thermal print elements. The shift register/drivers are contained in 7 hybrid circuits (80 bits each) mounted inside the printhead, they are connected to the thermal elements and to a simple PCB which joins the shift registers together by connectors similar to those used in the original HP41.
On the Australian museum site, you can get the 9876 service manual, and 'my' schematics of the 9845B. That may be a start as to how things work.
The printhead can be dismantled, but you have to go carefully. Remove the printer chassis from the machine, then remove the complete printhead assembly. Hold it with the front surface down, and make sure nothing is pressing on the electrolytic capacitors on the front of the printhead. Don't bother to remove the heatsinks, but carefully remove the screws on what is now the top face of the printhead. Slacken them a bit at a time, in a diagonal pattern, like taking the cylinder head off a car engine. With the screws out, lift off the metal block.
You can now see the 7 hybrids. Take them out carefully, keep them in order. They are all the same, actually, but it will help debugging if you put them back in the same place. Take out all the connector strips (there are 2 lengths -- 7 of one type and 28 of the other -- and HP say never to touch them with your fingers. That may be going a bit far, but I use tweezers anyway..). Now lift off the plastic frame that holds the connectors.
You can test the printhead elemenets using an ohmmeter between the printhead common connection (on the PCB) and each of the 560 pads that connect to the hybrids. My notes suggest that each element should read 110 ohms or so. If any are open, you need a new printhead (or at least the front block/thermal element part).
Clean all the pads and put it back together, try again. If it works, it was just bad contacts. If not and the defective columns are in the same places, take it apart again, take out the hybrid at one end, move the others along one position and put the removed one back at the other end. Reassemble and try again. If the bad columns have moved, then you have a defective hybrid. The only source is another printhead, of course, but you could move it to the right hand end, which would let you print short lines correctly.
If the defective columns have moved after the first reassembly, it sounds like bad connectors. Try cleaning them more carefully.