Shmiras Halashon / Part 2, Ch. 2 – 86

Even if a person’s thoughts are not completely devoid of sinful thoughts should not despair from learning Torah and doing mitzvas, as our Sages said, ‘One who comes to purify himself will be assisted’. If he truly seeks to purify his thoughts he will definitely see divine assistance, as our Sages said, ‘One should be involved in  Torah and mitzvas [even] for ulterior reasons, for through his ulterior motives he will reach altruistic motivation’.