The alarm didn't go off, so I overslept.

Literal

Alarm-clock [subj-が] not-rang [because-ので] overslept [regret-てしまった].

寝過ごす ('oversleep') is a compound verb: 寝る + 過ごす ('pass/exceed'). ~てしまった marks regret at the outcome. ~ので gives the reason naturally.