(I began this post yesterday, but mistakenly pressed “publish” when I intended to save it as a “draft.” Here, I reprise what I’ve already written and add to it, hopefully completing my point.)
“One of the primary purposes of tefillah
[prayers; especially liturgical prayers]
is to connect to Hashem through them.
This aspect of tefillah is often forgotten.
People are careful to daven at the right
time, with a minyan and…all the other
pertinent halachos of tefillah. But tefillah
is also a time for connecting with Hashem
and for conversing…with Him. This primary
aspect of tefillah should never be overlooked.” 
“…also a time for connecting with Hashem…”?
What other reason is there to pray?
Rabbi Biderman’s thoughts are based on the book “Noam Elimelech,” by Rabbi Elimelech Weisblum of Lizhensk (1717–1787), a leading Hasidic teacher in the generation following the Maggid of Mezritch (the 1st generation being the Baal Shem Tov himself; the 2nd being the Maggid; the 3rd being Rabbi Elimelech, Rabbi Shneur Zalman and the other talmidim of the Maggid). There are many famous stories about him and his brother, Reb Zusya of Anipol.
In this light, we can perhaps understand that the Noam Elimelech is speaking to an understanding of prayer that it’s fulfilled simply by meeting its formal requirements. Orthodox, and to a lesser extent Reform and Conservative Judaism, concur with this. What you “feel” in prayer is optional; what you “do” is what matters. The Hasidic movement in its inception was conceived as a refutation of this.
I’d point out here that this has little to do with the text of the liturgy. Reform Judaism, for example, might have believed that simplifying the liturgy and including more English would contribute to more “feeling,” but I don’t think this has been found to be automatically true. Likewise, Hasidic Judaism, especially in its formative years, added many customs to prayer, in the interest of increasing the “feeling.” Yet in later generations, even these customs could come to be performed only “rotely.”
Most individual Jews seek something in prayer. It might not be fully understood or articulated, but no one wants to say the prayers with unfeeling roteness. Rabbi Biderman is telling us that we are seeking, knowingly or unknowingly, a sense of connection with God.
Do the words of tefillah — liturgy — automatically connect us with HaShem?
In some ways, yes. There are stories of prisoners in concentration camps bartering a slice of bread for a few minutes of praying from a siddur (prayerbook):
“[Elie] Wiesenthal recalled that during his interment in the Mathausen concentration camp, something happened that nearly turned him away from religion forever. In the camp, there had been one religious man who somehow managed to smuggle in a copy of the siddur. Wiesenthal’s admiration for the man’s courage quickly disappeared when he discovered that the man demanded a payment from the meager daily food allotment each prisoner received. Wiesenthal recalled feeling disgust and thinking, ‘If this is how religious Jews behave, I’m not going to have anything to do with a prayerbook.’
Days after the Second World War ended, U.S. Army chaplain Rabbi Eliezer Silver came to Mathausen. Wiesenthal’s emotions were quite mixed when he met Rabbi Silver. He told the chaplain about the man who had bartered use of his siddur for food in order to explain why he, Simon Wiesenthal, no longer wanted to have anything to do with Jewish religious beliefs and practices. ‘What kind of a religion can this be, if a man robs people of their miserable, insufficient food allowance?’
Rabbi Silver asked Wiesenthal, ‘Why do you focus so much on what that man did? Why don’t you notice instead what all those people did? Aren’t you impressed that people who were nearly starving to death would be willing to give up their last piece of bread in order to hold a prayerbook even for only a few minutes?'” 
Those were people in the most extreme circumstances, for whom even a few moments of liturgical prayer gave them the peace of feeling connected with God.
But how much of our own mind and heart is engaged when we’re saying the prayers?
Much — perhaps all — depends on the thoughts that underly and accompany our prayers.
“The power and outcome of a person’s tefillah [prayer] is dependent upon the level of emunah [faith] a person has when he begins to daven [pray].” 
If one’s heart is open to God, the words of prayer lift it, and us, even higher.
How can we open our hearts to God?
In speaking of offerings in the Temple, the rabbis taught:
אחד המרבה ואחד הממעיט ובלבד שיכוין לבו לשמים
It’s all one whether one brings a lot or a little, if he directs his heart to Heaven. 
“…directs his heart to Heaven” is the rabbis’ idiom for turning the “heart” — the attention — away from any material thought, circumstance or condition and instead focusing on God alone. This is the cognitive essence of “faith” — undiluted confidence in God’s presence, power and willingness to help, followed (or accompanied) by letting go of all personal concern.
Faith is “letting go.” It is going beyond the thinking and feeling levels of the mind to its Divine Source; the “image of God” in us.
“Faith is the infinite in man reaching out to join its Source.” 
If true of sacrifices, it’s no less true of prayers.
If we are worried about a circumstance in our lives and say the words of prayers while continuing to wonder if God can help or if God will help, we have prayed, yes, but without faith. In that case, our prayer can be no more than a temporary distraction from our uncomfortable thoughts.
If instead, we say the words of prayers with our attention on God, unconcerned with our problems at all, we will feel the connection with God and the peace that is always the promise of faith.
Faith is not a matter of effort. It requires a change in thinking; more — a change in consciousness.
Faith can never be the product of our own effort or will-power. Our self-will is the very thing that stands between us and God’s Presence in and around us.
“Every man in whom is haughtiness of spirit, the Holy One, blessed be He, declares, ‘I and he cannot both dwell in the world [together]’…” 
God is revealed to us when we lay our own will — our “haughtiness of spirit” — to rest.
We must do this anew each day.
Yesterday’s faith is today’s memory; today’s convention. We might experience God yesterday, but today — we only have the memory of that experience; not the experience itself.
Today’s faith is always a new experience; a rediscovery of God’s Presence.
“Faith is based on revelation, but a revelation that takes place every day.” 
This “revelation” is the outcome of contemplation of God’s presence, power and goodness. All of the subject matter of kabbalah is really about the rediscovery of God’s presence each day.
We must “let go” and go beyond the intellectual or emotional aspects of our minds. The “infinite” in us must reach out to its Source.
Prayer, whether Orthodox or Reform or even non-liturgical, whether verbal or silent, if done with underlying faith, can connect us with God — reveal God to us again — every day.
(Torah Wellsprings; Collected Thoughts of Rabbi Elimelech Biderman, Shlita; on parsha Vayeitzei; c. 2016, p.1) The link works best if copied and pasted into the subject or search line.
“Torah Wellsprings” can be contacted at: email@example.com
 Rabinovitch, Hagaon Harav Gamliel; The Essence of Emunah; Rabbi Dovid Vatch, trans.; (no copyright indicated in book, but 1st impression 5770), p. 6
 Menachot 110a
 Lichtenstein, Rabbi Morris; Jewish Science and Health; p. 136
 Sotah 5a (elsewhere 4a)
 Lichtenstein, Rabbi Morris; Jewish Science and Health; p. 137