1995 honda accord manual trans no start but click sound there?

I have a 95 honda accord and car will turn lights on but wen i try to start all the car does is a click sound wen i push the car (since is mannual) i can make the car turn on i just replaced the alternator because the battery light used to come on and off after replacing the alternator the battery light didn't came on anymore so what else can it be please help!

If you can push start the car and it turns over and runs but won't start if standing still, it sounds like a bad battery or connection to the battery.
Not likely a starter since assuming everything worked prior the the alternator going bad.

The starter