There are so many wrong answers in this thread.
Quite possible, but your answers aren't helping either.
3d graphics, how long consoles had been around, the target audience, gameplay mechanics, education levels of programmers, diet preferences, etc. None of this matters as in what caused the decline. It was a certain set of actions and circumstances.
Consoles were actually the risky business, not the PC.
Hmm...no. At least this particular comparison is false.
Name me a console developer that's still around since the 1990s. Bonus points if you can name a console developer since the 1980s.
It's easy to come up with SEGA and Nintendo from the 80s, and Sony from the 90s, but whom else?
Then come up with a PC developer that's still around since the 1990s, and again from the 1980s.
What names come up? EA and Activision from the 80s, possibly even Atari. From the 90s there's Blizzard and Bethesda.
Here comes the clincher: How did the PC developers survive all these years, compared to the console developers?
The console developers that are still around today are megacorporations that trace their origins DECADES before their console involvement, in other fields. They launched successful consoles, but also unsuccessful accessories. The thing was, they had other markets to sustain them even if the console itself would fail. SEGA had to restructure itself after the failed Dreamcast launch, but they're still the biggest developer/distributer of arcades. Nintendo and Sony have taken their hits, but they're still around.
Now look at the home computer developers. Bankrupties, mergers, takeovers, acquisitions, mega-conglomorates, etc. ALL ACROSS THE BOARD. EA shifted its focus from being a developer to a publisher, with disastrous results for every studio brought under its wing. I honestly have no idea how Activision managed to survive into the 21st century, but it wasn't on the quality of their own games - they bought their talent from elsewhere, with Blizzard being their flagship. Atari has been restructured and reorganized so many times no one barely knows what's left of them, and Bethesda were bought out by ZeniMax, a media-orientated corporation.
You can bring up maybe two dozen consoles that failed due to the risky console market? I'm certain I can bring up over a hundred PC development studios that have failed due to the risky PC market, I can double that number if we expand that to include the now-deceased 'home computer' market in general.
This is because the entry-level capital needed to get into the console market, compared to the PC market, is so much higher. But the payoff is also so much higher, to the point that it's only the biggest and fattest cats that can afford being on the console market nowadays. PC developers, back in the day, didn't need to worry about developing hardware, so that's a large chunk of expense they escape. It's only today, when there's so little difference between PCs and the consoles, and with digital retailers being the de facto standard, that this is changing.
PC gaming today is built upon a mountain of corpses of development studios. The consoles, by comparison, have a few noticeable landmarks.
But back to the topic at hand.
Another factor no one seems to have noticed or addressed: Before Microsoft announced that they were entering the console market (1998 or thereabouts) the consoles and PCs were not really fighting one another, market-wise. PCs had simulators, grand strategy games and large, but slow-paced role playing games, while the consoles were focused on platformers, beat'em-ups, shoot'em-ups and 'hot seat' multiplayer games. Two seperate markets, one can claim. There were overlaps, sure. Popular console titles got converted to the PCs, but very few PC titles got converted to the consoles, it was mostly a one-way street.
Until Doom came along. People seem to forget how much Doom changed PC gaming. Suddenly a PC game was making console-level amounts of money. Better yet, it was a PC game that appealed to the console market. This got everyone's attention. Within 2 years Doom was available on every (major) console. This opened up the floodgates for PC titles to be either converted to consoles if they appealed to that market, or were developed for both markets simultaneously. Suddenly PC developers, with their lower level of capital requirement, were getting a foothold in the more lucrative console market. This led to many different people trying to come up with ways to combine the two markets, or become dominant in both. Guess who came up with the 'best' solution? Microsoft, by announcing that they, a gigantic OS developer with a small game design studio on the side, announced that they were entering the console market full-force, with a console that combined the best of both worlds.
It all sounds great until you look at the afterfall and the "side-effects": Everything that did not cater to the new X-Box would be left behind. If a game was too large, it was out, if a game had a control scheme beyond the capabilities of the X-Box controller, it was out. Niche genres that couldn't find a market on the console were out. "Conform or die" was the message of the day, and it was sent out to both consoles AND the PC. It didn't help either that the role model games for the X-Box console were FPS games, a genre that had already become diluted and overcrowded by the turn of the century on the PC. Here we had a console that not only created a bridge between PCs and consoles, but used that bridge to attack the PC market directly.
This is what Sony did NOT do, which is why the PSX and early-years PS2 are full of cool and innovative games - that mostly didn't see release on the PC. But by around 2005 even Sony and Nintendo were struggling a bit. Remember Buzz, Guitar Hero and Singstar on the PS2? That's Sony struggling to fight against the PC+console behemoth. Nintendo's Wii controller? The same. Eventually Sony caved in, released the PS3 and tried to cash in on the invasion of the PC market that Microsoft had spearheaded several years earlier. That kept Sony in the loop, but at the cost of a lot of the unique identity of the Playstation catalogue. Nintendo's market share may be dwindling, but they keep relevant because they're not following the leader like lemmings, they stick to their guns and have a good focus on the hand-helds...at least for now.
tl;dr - Doom was the herald, Microsoft the culprit, and the X-Box the weapon that brought along the decline, forcing others to contribute to it.