What are the implications for someone who intended 'Umrah, donned the ihram, and entered Makkah, but then took off his ihram without performing 'Umrah or entering the Haram due to exhaustion, and then performed another 'Umrah years later?

The obligation was to complete the Umrah (definition) because it becomes binding upon entering into its state of ihram (definition). One who enters ihram for Umrah remains in that state until completing its rituals. If the prohibited acts were committed due to ignorance of the ruling, then it is hoped that he is excused. However, he must repent for his negligence in learning the rulings of Shariah. He is not liable for anything regarding the prohibited acts unless they involve damage (like cutting hair or nails), in which case he must offer a fidyah (definition) (expiatory sacrifice) from the options available. However, if he was aware of the ruling, he must offer a fidyah for every prohibited act he committed. If the muhrim (person in ihram) had sexual intercourse, his Umrah is invalidated, and he must proceed with it, make it up, and offer a hady (sacrificial animal) for invalidating it. If he contracted a marriage during the period of ihram, the marriage is not valid and must be re-contracted.