Changing a capacitor isn't going to fix a duff coil, obviously, but it will address a defective condenser. No surprise there.
Sometimes, replacing a duff condenser will seemingly re-invigorate a coil that is past it. Many past-it coils show no HT continuity due to a small break inside, which the spark is capable of jumping . . . and they still deliver a passable spark at the end of the line, ie the Plug.
With a duff condenser as well as a past-it coil, the mag won't run right. With a new capacitor, of any sort, it might come back to life. But the break will get worse because there will be internal arcing in the coil.
So - the only sensible approach here, when starting to play, is to check for HT continuity as a first move. If there is none from the SLIPRING to the armature spindle ('earth'), then it MIGHT just be that the connection between the coil and the slipring is bad, and replacing the ring might restore things. But usually, it's a break in the coil and it's a false economy not to get it rewound. (Unless, of course, people have many years spare to get armatures out, and enjoy doing it.)
You'd expect to see, typically on a K2F, 5000-odd ohms from the brass part of slipring to armature spindle with everything connected. That figure might be as high as 7000 ohms on some windings, or as low as 4000 on some others, as the recipe of number of turns, wire gauges for primary and secondary etc, varies from rewinder to rewinder. (There are plenty of lower and higher numbers on other makes/models.)
Not to confuse this with LOW tension continuity . . . Between the base nut for the cb centre screw and the 'earth', there will only ever be about half an ohm as the winding (which lies under the HT one on the same core) has relatively few turns and is chunky. They don't fail often, in fact failure is rare as hens' teeth.
If it takes someone a year, even in jokey metaphor-speak, to get an armature out or opened up, that's probably not a good source of advice! It is actually pretty obvious which side of the low tension winding (and the condenser) is live and which is to earth, because one side is directly connected to the 'nut' on the cb centre screw via the condenser's tin case, and the earth side is attached to the armature brass end by the same tab that holds the condenser in place on a K2F (and most if not all Lucas). The earth side of the low tension winding is soldered to the said tab. Not hard to figure, and just needs eyes, or a £5 multi-meter for those who disbelieve what they see, to establish which is which.
In the event that the low tension wires are inadvertently reversed, the mag will still work. There are reasons why it's better to get it right, to do with getting the last bit of spark intensity and also the correct negative spark at the plug on singles - but you get one of each on a twin whether you like it or not.
There are no free lunches, and it remains true as ever that it is a BAD idea to start playing with anything if you haven't sussed out what to expect! Those of us who mess with these things every day try quite hard to explain much of this stuff, via websites, chats, face-to-face, whatever. But just as it's a bad plan to strip a gearbox, say, without taking bloody careful note of how the selectors and camplate work, which gears go on which shaft in which order, where the spacers and thrust washers etc etc go, it's a bad idea to start pulling the leccy bits apart without a care in the world. They'll come back and bite, guaranteed!