Okay, I began this adventure with a sink that would not drain on either side. We tried boiling water, plunging... So we took pipes apart to see if could find clog. When those were clear we checked all other drains for slow drainage. All working fine. We decided to snake the drain to pipes under and unseen. Then the pipe broke into the floor of the cabinet. Now I have a hole in the bottom of my kitchen cabinet were my drain pipe used to go. FYI I can see water in the drain in the hole . All pipes are plastic... Help...

You have a "S" trap,(see image) that should be replaced. Butif you see standing water in the open drain line you still have a clod in the line. Snake it out. Good luck, Tom