doing 100 pushups seems to make no difference in anything
Then you are probably doing them wrong.
Body in line, go down 3 seconds, stay down 3 seconds, then up 3 seconds.
Try doing 100 of those.
Positioning also determines which muscles are being worked out, if you are doing pushups for bigger biceps or something then yeah that's not happening.
Not to mention pushups are just one of the vast amounts of body weight exercises.
And last thing, I hope you don't mean just doing 100 push ups and that's all, doing a couple of any exercise one time isn't going to do anything.