I work out occasionally. Before I do, I drink a protein shake. I pour the powder into a large pitcher and mix it with two cups of milk. I quickly down the drink and hit the weights. About three or five hours later, I run to the bathroom with a horrible stomach ache and…well…diarrhea makes me poop. I suspect that I’m lactose intolerant which is fine and all, but I was just wondering if all the nutrients that I ingested from that protein shake went to, er, waste. Did my body still absorb the vitamins, minerals, protein, and carbs that the protein shake promised? Can anyone help me? Thanks. 
The speed of food through the body varies widely, from about 12 to about 24 hours. Even at twelve hours, your protein would have plenty of time to be digested. The material you rapidly dump right after your workout is not the stuff you gulped down right before the workout.
You can buy lactose-free milk. You can also buy lactase pills to replace the enzyme you lack, which makes you lactose-intolerant.
You didn’t ask whether the protein shake is useful for muscle growth, and I didn’t address that Pandora’s can of worms.