"I give myself unto prayer." ~ Psa. 109:4
Whenever you read such terms in scripture as Solomon's, "I sought in my heart to give myself unto wine"; Paul's "Who being past feeling have given themselves over unto lasciviousness"; and Timothy's (speaking of Christ), "Who gave Himself a ransom for all," it usually means completely, without reservation.
This is the meaning of David's statement. He was a man given over entirely to prayer. Prayer was not a part of his life; his, was a life of prayer. Like Nehemiah, Daniel, Hannah, Paul, and his Lord.
When prayer ceases to be a category in a saint's life, and becomes like their very breath, communion and prayer run together.
You can always spot a professing Christian in whose life prayer is cataloged. Invariably, in a crises, you'll hear the telling statement, "Well, all we can do now is pray." Like we could every do anything else.
It is not the use of human means, then prayer. It is prayer, followed by God directed means.