Your plant shows a significant amount of green foliage and appears to be alive. Try removing the old and wilted leaves to allow new foliage to emerge, place the plant in full sun, and follow a regular watering schedule.
I think that it comes down to the winter hardiness of the Agapanthus. The Agapanthus or the Lily of the Nile is a South African native. There are two kinds of Agapanthus: the evergreen type is hardiness zone 8+ and the deciduous type which dies back in winter is zone 6+.
In Toronto we have hardiness zone 6b and in the GTA zone 5b. Too cold for Agapanthus.
It is suggested that you put the evergreen Agapanthus in a pot and take it indoors for the winter. Treat as a house plant.
A deciduous Agapanthus in a pot can be placed in an unheated garage or frost free area. Around the beginning of May, place pot outside in a sheltered area.
For more information on growing agapanthus, check out this link to a previous post.