Ethical Dilemma: Should I draw?

Ok, here is the situation and please tell me your viewpoint. 

I am playing a 10m Live Game here on Chess.com. 

Lets say we are in middlegame and opponent is winning, better positions of pieces, took more pieces that I did but has little time left, lets say 2mins and I have 6mins. 

And then he blunders, he looses his Queen and the Game would have been equal if there wasnt the time. 

So, I am thinking, should I offer him a draw or try to win on time?

The only ethical "dilemma" here is whether or not you should have resigned when he was a Queen up. Your question is ridiculous.

Time is part of the game. If your opponent plays a 10-minute game then they have agreed that the time is part of the game. Good time management is a critical skill to have in chess, and I think that punishing opponents for bad time management is also a good skill to have.

I personally don't really like winning on time as much as winning by good play, and might occasionally offer a draw if they outplayed me in the position, but I think it's really just being extra nice to them.

Now a mouseslip is a different issue...

There is no ethical dilema here.  You are playing a game to win.  Blunders are the responsibility of your opponent.  If you are a queen down and still playing, you are hoping for a blunder, either that he hangs a queen, allows a one move mate, or stalemates you--and that's fine.  Even misclicks are just a thing that happens, similar to a bad call by a referee in sports.  I had one this week.  Wanted to play queen takes.  Instead dropped the queen one short, not only failing to take but able to be taken.  Annoying.  Not the end of the world.  Play on.

Blunders that occur first aren't more important than blunders that occur later... ethically speaking (lol).

Apparently you are not familiar with Maslow's Heirarchy of Blunders!

I've had it happen a few times where I'd been playing a long series of games with the same opponent and consequently I was having a lot of fun and had a lot of respect for their ability.

Only in these cases, and partly as a sort of self indulgence, I will offer a draw if they make an obvious mouse-slip type of blunder and now it's an equal position but they have very little time.

But in at least two of these instances my opponent declined and resigned!

There is no ethics in Chess. Only death.

I would not offer a draw because my opponent has committed a major blunder.  I have resigned before when my opponent was solidly winning until committing an obvious mouse slip.

10 minutes is blitz. There are no ethics in blitz. Take the win because if roles were reversed I can almost guarantee your opponent wouldn't offer you a draw. My last blitz game should've been a loss, I got in time trouble so I went kamikaze on his king wound up down a piece after having a huge advantage, then came back and won after checking him a billion times and forcing him into time trouble until he blundered. That's blitz, fight til death and take every win you can get.