What is the legal ruling for someone who wakes up without an alarm half an hour after sunrise, despite having woken up half an hour to an hour before that without feeling the urge to get up?

If you wake up half an hour before sunrise, your prayer is valid. However, if you wake up after sunrise, there is no sin upon you because the pen is lifted from the sleeper until he awakens. If you wake up after sunrise, first pray the two rak'ahs of Fajr, then the Fajr prayer.