We know he renounced lust because he never consummated his marriage, and he would at times be so caught up in samadhi that his cloth would slip off, and there was no sexual significance in that. It is said he was like a child in this respect.
We know he renounced wealth and greed, because one time when the authorities told him he had to leave his home at Dakshineswar, he got up without a second thought and started to leave, although he had no place to go. Also, as a youth, he had no use for a bread-winning education.
We know he renounced pride, because when Naren told Sri Ramakrishna he shouldn’t care about him so much, Sri Ramakrishna didn’t argue, but asked the Divine Mother if it was true. Also, Sri Ramakrishna did not like anyone to call him Guru, and he didn’t like anyone to write about him in the newspaper.
I have been aware of all of these incidents for a while, but when you take them together, I think they prove the point that Sri Ramakrishna lived a life of great renunciation.