Today, my wife called me in the kitchen when there was water leaking out of our pipes below the kitchen sink. I figured there was a clog, so we threw some drain cleaner down there and did some plunging. No big change and the pipe was still leaking ,starting at the overflow.

So I got under the sink and took apart a couple of the joints and found some crud, and removed it. Put everything back together, and it still leaked. So I went went beyond the overflow and took that apart and found some more crud. Then I did some snaking with a wire hanger straightened out and got a little more.

I then put everything back together and no leaks. But now, nothing will drain. Any help?

Your snaking with the coathanger probably dislodged or impacted the crud and it has blocked the drain. Get a snake and go farther, coat hangers are only good for 12" and very small items if that.

Stop with the chemicals and hang up the coat hanger. Fill the sink and let it drain slowly to get rid of the chemicals. Opne and remove the trap and rod straight into the wall with a 1/4" snake or rotary drum auger. Amazon.com: drum auger: Tools & Home Improvement