Ligustrum are notoriously hard to kill so if is not showing any activity over ground, may be working hard building roots at this moment.

The shadow is not really the problem. They love full sun, but can stand a lot of shadow. The lack of water or nutrients may be. Let it fully submerged in a bath for one hour. If is still alive, the bark or stems will turn greenish and new leaves may appear in a few days.

Sinense is semi caducifolious (if I remember correctly). Are you in spring or in autumn currently in your timezone?

(If you have pets take in mind that this is a poisonous plant with poisonous fruits only allowed for birds).