I am under the impression that if there is a chain resolving, nothing can happen until it's resolved. I was playing a rather interesting combo deck involving self destruct button, and at one point during the chain's resolution both players were at zero LP. The other player wanted to end the game right there. I said no. My argument was that nothing can happen ( not even the end of the game) until the chain is completely resolved, then any other effects go through (namely the game end). Could I get some oppinions on this, maybe even an official ruling if anyone can find one and cite it?

I just read about this. The game can end in the middle of a chain. In your situation, your opponent was correct in saying that the game ends if both players' lp were at zero. The specific example I read was if both players Sangan were destroyed. The turn player's Sangan gets its effect as Step 1 and the opponent's Sangan is Step 2. Of course we all know that chains resolve backwards, so the opponent gets to search first. He/she pulls the last piece of Exodia before the turn player get to pulls his/her last piece but b/c the opponent has all the pieces he/she wins.

Try not to get it confused with card effects. A game cannot end in the middle of a card effect (example: Drawing the last pieces of Exodia before discarding for the effect of Graceful Charity) but it CAN end in the middle of a chain. Hope this helps!

Aren't Exodia and life point depletion two different win conditions? What if someone activated a life point gaining magic card, and then the opponent chained ring of destruction or something which would end up taking all of both player's life points. Wouldn't you then resolve the life point gaining magic card next? Or is that impossible or an unrelated situation for this topic?

no its isn't different.

once 1 or both players satisfy a win/loose condition, the game ends immediatly. unless your in the middle of resolving an effect or in the middle of a summon.

win/loose conditions have the same timing as continuous effects, they jump right in between chain links if necesarry. they are not effects with speeds, they don't have to have a chain link, they don't have to wait until after the current chain. they just have to wait until after the current effect.

so if you use self destruct button, immediatly after it resolves and makes both players lifepoints 0, the game ends in a draw. anything else on the chain is irrelevant.

Oh, okay. Just checking, because I wasn't fully sure with the other guy's explanation.

Ok...... just to walk a little bit deeper in the matter, it's not that the nothing can happen during the current chain, its that ANY NEW EFFECTS triggered DURING the current chain can be resolved in the moment or the chain in progress it has to create a completely NEW CHAIN........
i.e.:
Field:
Player A: Cyber Jar (set), Torrential Tribute(set)
Player B: Desert Sunlight (set)

Player B's turn:
- Player B: Summons Mad Dog of Darkness
- Player A: Activates TT in response to the summon
- Player B: Activates Desert Sunlight flipping Cyber Jar face up.

Resolution:
- Desert Sunlight flips Cyber Jar (Cyber Jar CANNOT ACTIVATE ITS EFFECT AT THIS TIME, so not being able to activate it forms a NEW CHAIN, being its effect Chain Link 1).
- Torrential Tribute destroys all monsters on the field.

NEW CHAIN:
- Cyber Jars effect activates..... blah, blah, blah.........and so forth............

now in your case losing_lenore, SDB WAS IN DEED PART OF THE CURRENT CHAIN, so as soon as the SDB fully resolved in the middle of the chain both players get their life points reduced to 0 and a tie is declared.