Having found me to be an alcoholic, she did not like me and spurned my offer. But I would attempt
(to warm up to her) - this is incorrectly used in this context - She needs to starting warming to you!!
but nothing encouraging happened. Now the story has taken an unusual turn. Things have changed for the better. Now she has realized that I am a changed person and so (has) started showing affection, which of course does not surprise me much.