As a Spanish speaker, I would interpret that as:
"He/she wanted to hit me hard."
"Dar" in Spanish generally means "to give", but as a colloquialism it can be used to mean "to hit". As in:
Te voy a dar con el bate. ↔ I'm going to hit you with the bat.
In review of the original context, which I had not seen before, (not sure why) the sentence does not really make a lot of sense to me. I have the following 2 guesses. 1) The sentence is poorly written (the grammar, for once, hints at this.) It meant to say something like "Cuando falleció, me quise dar fuerte en lugar de ponerme a llorar o gritar." Meaning: "When he/she passed away, I wanted hit myself hard instead of crying or screaming."
2) "When heshe passed away, heshe wanted to hit me hard instead of making me cry or scream." This one is the least likely of the two in my opinion. It might be in reference to how the passing character aimed to hit someone else with his/her last breath. If I had to guess, I would interpret it as per my first guess. Then again, the original context sentence structure does not make a lot of sense to me as a Spanish speaker. And it does not even sound like it is due to more formal, archaic or dialectic interpretation. It just sounds weird.