It kept barking at me at the gate and wouldn't let me in.
Literal
Gate [gen-の] place [at-で] me [at-に向かって] kept-barking-[て] in-let-[not-てくれなかった][explanatory-んだよ].
~に向かって ('facing toward, directed at') marks the target of a directed action like 吠える ('bark'). 吠え続ける ('keep barking') uses the auxiliary ~続ける ('continue to'). The negative ~てくれなかった ('did not do for me') marks the refusal of a requested favor.