"I do not have a key."
Translation:저는 열쇠가 없어요.
있다 and 없다 roughly translate as: to have/have not, to exist/not exist, or to be/not be at a location. Each of these sound like active verbs, but 있다 and 없다 are actually descriptive verbs (adjectives).
Only active verbs can act on an object. You can drive/clean/crash a car, but you can't fast/pretty/bad a car. So 을/를 isn't the correct particle since its purpose is to define objects for active verbs.
Instead, 있다 and 없다 always pair the object with 이/가 for sentences related to have/have not and exist/not exist.
For Japanese speakers, 이/가 is similar to the usage of が with あります/います.
The particle 에 is for those times 있다 and 없다 mean to be/not be at a location.