The elven gods had a duality to them, a 'normal' elven component and a dragon aspect. We know that Andruil went down into the abyss, and I believe there's convincing evidence that she brought the taint back with her. Mythal used her dragon form to fight Andruil, eventually winning and taking the knowledge of how to get into the abyss from her (side note: if Sera is Andruil, which I don't think she is but I do think the theory is a hoot so I might as well incorporate it, perhaps Mythal took more knowledge than just how to reach the abyss, which is why Sera (or the spirit of Andruil inside her) doesn't really remember anything of who she is). By this time, we know that Andruil's lands had been ravaged by plague, and she'd been driven mad for longer and longer periods.
I believe the taint spread amongst the elven gods, and it's the madness that ensued that caused them to devolve so much into fighting amongst themselves (and is what likely led to Mythal's murder). I think that Fen'harel devised a plan to end the fighting before anymore of the gods were killed, but since he had no way to cure the taint he had to find another solution. He found a way to separate out the two components of the gods: their main elven form and their dragon aspect - and that dragon aspect remained tainted, whereas the elven aspect didn't. But without both parts the god is not whole, and wouldn't function - perhaps that dragon aspect housed much of their magical power too. So Fen'harel locked them all away: the 7 remaining gods up in the heavens, and the 7 dragon aspects (the 'forgotten ones') down in the void/abyss. This bought him time to try to find a cure for the taint, so he could cure the dragon aspects/old gods/forgotten ones, and reunite the 2 halves of each god and bring them back. This is something he still hasn't found the solution for.
I believe he also sealed away part or most of Arlathan, and that is what people believed to be the Golden City. But, when he sealed it it was already black, corrupted by the taint. We've been told that the fade takes on the shape of the things people want to see, and reflects their reality through twisted, misunderstood versions of their memories and dreams. I think this is a two-way street, and that not only does the fade take on aspects of people's memories and dreams, but people see what they expect to see, albeit in a slightly weird and warped way that doesn't quite reflect reality. I believe people talked of a 'Golden City' in the fade because of a mixture of things: up until then, Arlathan had been (according to my theory) the most impressive city ever seen, and as what was likely the seat of Elgar'nan, it was probably golden (he was the sun god, after all), so it would make sense that a reflection of that was in people's minds and that it would be represented in some way in the fade; as time went on, it was simply expected to be there by people going into the fade in their dreams, whether it was there or not, and whether it looked like that or not. Over history, as Andrastian religion came into existence, tales of a great Golden City being the seat of the Maker became common belief and knowledge, and so it continued that that was what people expected to see in the fade, and this is therefore what they would see in the fade.
When Fen'harel locked away the real Arlathan into the portion of the fade no one could get to, it was blackened, tainted, corrupted, but no one noticed, because they didn't expect to see that, they expected to see a Golden City, and that's what they saw. It was only after the magisters went into the fade in their physical forms - the first time in recorded history that had happened - and they saw the thing they expected to be a golden city was actually a Black City, that people's perception changed, and everyone - the magisters included - did the only thing they could logically do: they assumed this was the Maker's Golden City turned black. People in the Chantry blamed the magisters, claiming the Maker turned it black because of them, but the magisters knew better: they were correct when they said it was already black. It was also tainted, of course, and so they were tainted by it - presumably the magic involved was unlike anything we've encountered, and it's through this that they became the first human darkspawn.
All of this explains why Solas is grumpy about the Wardens. As they hunt down and kill the old gods, they're killing the dragon aspects of his brethren, stopping him from being able to find a cure and reunite them all, to undo the terrible mistakes of history. The darkspawn are drawn to the old gods/dragon aspects because they are powerful loci of the taint, and when they find them they don't create an archdemon - because the dragon is already what we think of as an archdemon - but they do set one free, which then goes rampaging across the world fuelled by a blind rage for a war (with the other elven gods) that it no longer remembers (because it isn't a whole being). Kill all the old gods, and not only has Solas failed in trying to stop the elven warring, but he's failed to bring them back, he's indirectly caused some of the worst atrocities to have befallen the world (the blights). He's also grumpy with the Grey Wardens because they think that once all the old gods are dead there will be no more blights. Well, that is flat out wrong. The remaining darkspawn simply won't have their powerful loci of the taint to move towards, and they won't follow an archdemon across the continents. But they and the taint will still exist, and without something to focus on they'll disperse, creating a sort of perma-blight. Whether that would be more manageable to control or less so than a full-blown blight I don't know, but it still wouldn't exactly be the preferred solution to the problem.
There are likely plenty of holes in this theory, and I don't really mind. I have a blast speculating, and coming up with ridiculous ideas (you should hear my theory about the dwarves). Sometimes I get things right (I guessed who Flemeth and Solas were), sometimes I get things very wrong, but I don't mind when I do. It's fun to guess, and to read other people's ideas. But anyway, that's my theory about the archdemons and the elven gods.