Can one begin with faith and good deeds and then repent, due to an inability to fulfill the condition of remorse in repentance?

Your thought that you cannot feel remorse is a misconception, for remorse is necessary for every repentant person. It is the heart's pain over committing a sin and wishing not to have done it. Knowledge of the harm of sins and their evil consequences necessitates remorse. Continue in your repentance, and turn to your Lord, striving diligently in good deeds, regretting past sins.