The effect of "Starliege Paladynamo" does not activate unless it's destroyed by the opponent while the owner controls it. Therefore, if a "Starliege Paladynamo" that is on the opponent's side of the field is destroyed and sent to the Graveyard, its effect does not activate.[1]
If at the time of the resolution of the effect of "Starliege Paladynamo" the targeted monster's ATK has become 0, the effects of the targeted monster are not negated.[2]
The effect of "Starliege Paladynamo" that makes the ATK of the targeted monster become 0 and negate its effects is an Ignition Effect that can be activated during the Main Phase. Therefore, it cannot be activated during the opponent's turn or during the Damage Step.[4]
References
↑Konami OCG Card Database: If a "Starliege Paladynamo" you own is on the opponent's side of the field, and is destroyed by a card effect controlled by either player and sent to the Graveyard, does its effect to draw 1 card activate?
↑Konami OCG Card Database: If at the time of the resolution of the effect of "Starliege Paladynamo" the targeted monster's ATK has become 0, are the effects of the targeted monster still negated?
↑Konami OCG Card Database: Can the effect of "Starliege Paladynamo" that makes the ATK of the targeted monster become 0 and negate its effects be activated during the opponent's turn or during the Damage Step?