Even when we don’t have kavanah, we should continue davening. A hint to this concept is in the piyut (Hoshana Raba), ולב לב בלא שיח לך שופכים, "They pour out their words, without a heart and with a heart." We can explain that this refers to people who, although they don't have a heart when they daven, they want to daven with kavanah. Their desire to daven properly should be enough for נא הושע, that Hashem should answer their tefillos.
Another counsel for tefillos to be answered is to daven with kavanah. As it states, ואתחנן לאמר ההיא בעת 'ה אל and the roshei teivos of עתב אמרל היאה spell ב"הל, the heart, indicating that Moshe davened with all his heart and soul (Chida, Nachal Kedumim, Ve'eschanan 1).
The Baal HaTurim writes that the gematriya of ואתחנן is שירה. He explains that Moshe said שירה, songs of praises to Hashem so that Hashem would listen to his tefillos. We do the same as we begin our tefillos with pesukei d'zimra and praises, and that helps our tefillos to be answered.
The Imrei Shaul of Modzitz zt'l explains that praising Hashem implies that he is confident that Hashem will help him. So, he sings and praises Hashem even before salvation comes. That trust is mesugal for his tefillos to be answered. As it states (Tehillim 106:44), וירא, Hashem checks to see whether בצר להם, when people are going through hard times, רנתם את בשמעו, they are already praising Hashem and thanking Him for the salvation that they know will come.
