watched a lot of video tutorials but nothing helped

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i searched on youtube how to replace old 1970s door knob with no visible holes outside. but nothing similar with my old door knob. the key no longer works. it can no longer open the door lock. though i can open the door lock and close it from the inside. i bought a new door knob that i still can't install for now. i took a picture of the inside of the old knob. there's what it seems like something I need to push down to loosen the front knob. but maybe because it's too old that's why I had problem pushing it down. there's error on the page when adding the picture