You ask this question on the Friday of parasha Tzav. In a dvar Torah on that parasha, the Lubavitcher Rebbe (Likkutei Sichot vol I, pp. 217-219, cited in R Sachs' Torah studies p. 159) comments on the verse Vayikra 6:6
אֵ֗שׁ תָּמִ֛יד תּוּקַ֥ד עַל־הַמִּזְבֵּ֖חַ לֹ֥א תִכְבֶֽה
Fire shall be kept burning upon the altar continually; it shall not go out
and on the Talmud Yerushalmi comment on this verse (Yoma 4:6)
"Continually - even on Shabbat; continually - even in a state of
He writes that every aspect of the physical Sanctuary has its counterpart of the inward Sanctuary within the soul of the Jew.
His heart is the altar. And corresponding to the two altars of the Sanctuary, the outer and the inner, are the outer and inner levels of the heart, its surface personality and its essential core. The altar on which the continual fire was to be set was the outer one. And for the Jew this means that the fire of his love for God must be outward, open and revealed.
To the man who has traveled so far on the part of separation that he feels he has now no link with God, the Talmud says "It shall not go out - even in a state of impurity" for the fire does not go out. A spark always burns in the recesses of the heart. It can be fanned into flame. And if it is fed with the fuel of love, it will burn continually.
The essential implication of this is that every Jew constitutes a Sanctuary to G‑d. And even if he learns Torah and fulfils the commandments, if the continual fire is missing, the Divine presence will not dwell within him.
The Jew must bring life, involvement, fire, to the three aspects of his religious existence: Torah, prayer and the practice of charity. (Pirkei Avot 1:2)
see the full dvar Torah for more details.
Now in my personal experience, the way to "warm up" divine service when things get tough are
in terms of Torah learning, to try and learn Torah that warms the heart, which depending on the individual can be the weekly parasha with a good commentary, hassidut, or Mesilat Yesharim
in terms of prayer, to pick up one prayer (starting with shema and shmonei esrei) and to slow down massively for 5 minutes to really focus on the words and try to understand the meaning of the prayer. Some do this with a different part of the prayer every week to cover enough material very slowly over the week. Other tools that can help are an interlinear siddur to help understand the Hebrew or a book on prayer (e.g., Praying with fire)