After a pm exchange with Allan, here are some corrections/explanations about the translation to "Todavía cantamos".
Each verse follows (gramatically) the chorus, so they're to be understood as

...Todavía esperamos...
1- A pesar de los golpes
que asestó en nuestras vidas
el ingenio del odio
desterrando al olvido
a nuestros seres queridos.

... we still hope...
3- despite of the blows
that the inginuity of hate
gave (in)to our lives
by bannishing into oblivion
the ones we love.

...todavía esperamos...
que nos den la esperanza
de saber que es posible
que el jardin se ilumine
con las risas y el canto
de los que amamos tanto

...we still wish...
to be given the hope
to know that it's possible
for the garden to be illuminated
with the laughter and the singing/song
of the ones we love so much...

Allan asked, "Also, the first line of the chorus ... well, I have to wonder what meaning was intended. If we say, 'We still wish,' it only appears to mean that we simply continue to wish. If we say, 'Still we wish,' it means something more toward 'Yet we wish,' or that despite all that has happened, we continue to wish. My idea of the song causes me to think 'Still we wish ...' sounds more in keeping with the spirit of the song; but I really cannot say with any certainty."
I answered, "If we consider that 'todavía' means 'toda vía' = all/any way = anyway, 'still we sing' is closer to what is meant but it could also be understood as 'we still sing' since 'todavía' also means 'still' = we continue. 'Still we sing' could be 'Por lo tanto cantamos' or 'Sin embargo cantamos' but there wouldn't be the concept of keeping on singing continuously and 'we still sing' could be 'cantamos todavía' but there wouldn't be the idea of "in spite of all" . Since 'todavía' goes first, I feel it as if it were "yet we still sing".

One thing that can't be rendered in English is that the Spanish verb "esperar" means both "to hope" and "to wait" (though if you think about what "to hope" means, it's "to wait for something-you-wished-would-happen to happen" if I can put it this way)