。
By the time I woke up, it was getting on toward noon.
Literal
Eye [subject-が] awakened time, noon [at-に] was-about-to-become.
なりかかっていた is the past resultative of なりかかる ('be about to become, be on the verge of becoming'). ~かかる attached to a verb stem means 'start to / be in the middle of / be about to' — a transitional aspect that English has to spell out with 'was starting to.' Paired here with the past resultative ていた, it pushes the reference time forward: by the time of waking, noon was already approaching.