2003 Honda Civic EX won't start

I have a 2003 Honda Civic EX and it won’t start if you disconnect the battery negative then positive let it sit for a couple minutes then reconnect it positive and negative you get all the lights back on the dash everything works till you turn the key over one time then it goes click and all lights disappear till you go back and do the exact same thing with the battery again and it resets it somehow and all the lights come back but till you turn over the key one time and it just goes click and I cannot get it started I do not know what to do with it I took it to the auto parts store they told me that it was an alternator which it didn’t happen to be obviously I put in a new alternator and it’s still doing the same thing they told me the battery was 100% but when I look in the battery it’s actually an open cell it was looked almost dry inside the battery