I like it. I really do.
From the tangled boughs of my heart ached cry,
My spirit, though a mired with life’s fevered din,
Seeks Your consul; relief, sweet relief forever nigh!
I'd drop the "a" prior to mired. If you need a beat there, I'd suggest enslaved or enraptured for the line, but I do prefer the time mired for its connotations. I get what you're doing, but the rhythm breaks a bit for me there.
In poverty, You found me, an unmoving peasant.
You raised me up; taught me Your love song!
Prayers of thanksgiving drenched my lips incessant…
"You raised me up" makes me think of the horribly trite song by Josh Groban - it's his fault, not yours btw. I'd almost like to see either an archaic expression here or just a change away from that line. I like the imagery, just not the diction, in other words. Love the two other lines that frame it!
Where have they all gone,
But, where have they all gone?
You may have a purpose I overlook here, but I'd add a simple "Lost?" or "Gone?" to complete this stanza and maintain the triune structure of the stanzas. I think visually it speaks to the obvious trinity always being present even in my moments of despair or forgetfulness. It would also make the poem 7 stanzas long.
I don't want to seem to harsh a critic, as this is an excellent start and I do ask to see more!