In Spanish, you cannot say "No me gusta lluvia", so "No me gusta la lluvia" means both "I do not like rain" and "I do not like the rain".

I'll take a stab at it but hope a native speaker will weigh in. The order is important here. It's "A mí no me gusta la lluvia". And I think that in Peru at least, if this is the beginning of your thought, the "a mí" is normally how it starts to the point that if you start out with "me", it sounds like something is missing.