Prayer Without Worship

לְאַהֲבָ֞ה אֶת־י״י֤ אֱלֹֽקיכם וּלְעׇבְד֔וֹ בְּכׇל־לְבַבְכֶ֖ם וּבְכׇל־נַפְשְׁכֶֽם רש"י - עבודה שהיא בלב. בלב – זו תפילה

Obviously, if the point of prayer is עבודה שבלב it is an integral part of prayer.  The question is if prayer without intent isn't prayer at all or is just a prayer in an incomplete form.  In other words, is the קיום of prayer  עבודה שבלב but there is a chaftzah, a maaseh mitzvah of prayer irrespective of  עבודה שבלב or without the עבודה שבלב it is not a cheftzah of prayer at all.

The Briskor Rav was asked according to his father's yesod, that one must have the knowledge that he is standing before the King when praying Shemonei Esrai, if many people don't have that intent, does it come out one prayed without a quorum because it is as if they didn't pray as well?  The Rav responded that even though a prayer without that intent is incomplete, it still is a chaftzah of prayer (cited in Shoalin V'dorshin of Rav Schlesinger volume 9 siman 4, see there his own answer.)  He cited proof from the Keter Rosh of Rav Chayim Volozhiner:

We see although a prayer without concentration is not optimal, it still counts as something.  (What is the comparison between korban vs. that of mincha needs an explanation, I don't know why it is that way.) 
The halacha is that if one doesn't have concentration in the first beracha of Shemoni Esrai, one must repeat the prayer.  The Tur writes that nowadays when proper concentration is often lacking, one should not repeat Shemoni Esrai on account of a lack of concentration.  The Beur Halacha beginning of siman 101 points out that from the Chayeh Adam it sounds as if this is true even if one is aware in the middle of their Shemoni Esrai of their lack of intent in Avos.  Asks the B.H. how can we tell the person to go ahead and finish their Shemoni Esrai, saying for sure ברכות לבטלה just because repeating Avos may be to no avail?  Answers the Steipler (Berachot #27) because although prayer without intent is not עבודה שבלב, it is still a cheftzah of prayer.
There is a lot more on this, תן לחכם וכו.