Late to the party, but I figure I'll give my two-cents' worth on the topic.
For one, I'm not sure if this has been corrected or not, but whoever thought Dante is only 10 years older than Nero? Doubtful. Capcom never official stated his age, but it's more likely that he's in his late 30's, which would make it possible for him to be Nero's father.
I believe the game's director said DMC4 takes place ''roughly ten years after DMC3.'' Since Dante is 19 in DMC3, that makes him about thirty in DMC4. And to be honest, he looks like he's thirty, not forty or something. Also, look at Lady and Trish. They both seem about 30.
In the case of Vergil being Nero's father, despite his apparently cold demeanor, it's entirely possible he got someone pregnant before the events of DMC3. There is a lot of evidence to support Nero being his son but admittedly, that same evidence could point to even Dante and Sparda. One of those things is Yamato; Yamato originally belonged to Sparda who passed it down to Vergil. So when Yamato reacted to Nero dying and aided him in awakening his devil, it could be either because it belonged to Vergil, or because Nero is of the Sparda bloodline, period.
Nero seems to be aided by Vergil when he goes into Devil Trigger. This seems obvious when you play as Nero in DT, since he says some of Vergil's lines: 'blast', 'begone', and 'jackpot'. That last word is one Nero could never have known to be significant. Only Dante and Vergil said 'jackpot', and it should only hold meaning to them. Nero's DT awakened when he got hurt by the demons who were 'made out of parts of Nero Angelo' (the Bianco Angelos). So he probably went into DT either because he got mortally wounded, or because he got hurt by something that came from his own bloodline (Nero Angelo/Vergil). It's important to note that Dante got his DT when he was hurt by his own sword, which was left to him by Sparda. Maybe the same thing happened here, with something containing parts of Sparda's bloodline (Nero Angelo) wounding Nero and making him go into DT. Then the Yamato responded to Nero because... well, either because he's a demon or because he has the blood of Sparda's family line.
If Sparda did not die, however, it may have gone something like this: Imagine Sparda recovers and returns from whatever he was doing and wherever he disappeared to-just to hear the rumours that Eva and his sons have been killed (obviously his sons aren't dead...or at least not both of them). So, he grieves. After some time passes, he may very well settle down with another human woman, and pass on his legacy further before disappearing for good.
No offense, but there is no way he would not have noticed Dante or Vergil being still alive. Dante pretty much leaves a trail wherever he goes, and as far as I know, he's very well-known. Just the fact that he has an agency should tip Sparda off. Or Vergil resurrecting the Temen-Ni-Gru in DMC3.
Again, I'm leaning more toward Nero being Vergil's son. As far as we can tell, despite how powerful he is, Nero is still not at the level of Dante or Vergil, and his devil trigger is far different from theirs-which I think means he is only a quarter devil. Not to mention how his arm changed sometime just before the events in DMC4.
Since Nero wears blue and red and wields the Red Queen and Blue Rose (Sparda hints) while his Devil Trigger is blue and looks a lot like Vergil's DT, I'd say his Devil Trigger is influenced by the Yamato (or Vergil, if part of Vergil's soul is inside the Yamato, which seems to be the case). His arm doesn't make sense to me, though. It seems to be part of him, like a partial Devil Trigger.
Apparently more of this is touched on in the "Deadly Fortune" series that has yet to be released in any other language besides Japanese (though some people have translated bits and pieces). However, there's controversy about whether those novels are considered canon, or not.
I heard that that novel is basically canon, since it was written by the same person who wrote DMC4. But then, that would make Nero Vergil's son, which doesn't make much sense if you consider their age. Nero is 19, Vergil would be about thirty. So... Vergil conceived Nero when he was 11... yeeeah. It also would make it odd that official artwork of Nero shows him sporting a full DT body. If he's only a quarter demon, shouldn't he have a mostly human body? I know he does, but the arm doesn't make sense. And just the fact that his artwork shows him as a full demon is very odd.
I still think it would be the most logical if he turned out to be an experiment, made by combining Dante and Vergil's genes. That would explain why he's blue and red, why Berial says he's ''just like he was'' (Sparda), and it would make sense for the game's plot. I mean, Nero is in THE place where Sparda is worshiped. If he's only Vergil's son, wouldn't that make it weird? All this Sparda symbolism, even a fight with THE SAVIOR (Sparda), and yet, Nero is just Vergil's son? Not really appropriate.
