Furnace won’t stay running and when the blower motor runs it sounds like it is sucking up water
Your furnace drain is clogged

No, seriously.  From the appearance of this furnace, it is a condensing (aka "high efficiency") type furnace.  In a non-condensing ("medium efficiency") furnace, the water produced by combustion goes out the flue as vapor along with all the other things that you don't want in your house.  However, condensing furnaces extract enough heat from the burner exhaust gases that the water in them largely condenses out as liquid, which is drained to the sewer system, while the rest of the gases go on their way out the vent pipe.

As a result, a condensing furnace like yours needs to have a free-flowing drain to function.  If the drain is clogged, condensate backs up and into the furnace as you are observing, causing it to shutdown for one reason or another.  Fixing the clogged drain with a thin plumber's snake or compressed air (not Draino, as you don't want drain cleaner getting on furnace parts) should get the furnace going for the moment, but you'll want to have a technician examine your furnace closely at the first opportunity to make sure that condensate hasn't gotten places it shouldn't have (such as into the electrical workings or the gas system).

The owner's manual recommends inspecting &amp; cleaning the condensate line semi-annually.