Dishwasher not actually washing dishes, soap left behind
There should not be a problem with any normal dishwasher detergent - powder, liquid or "pods". Plus a dishwasher even in simple rinse mode (deliberate or "oops, forgot to put in any detergent") will usually get most of the crud off the dishes.

Detergent left behind, as well as dishes not being clean, points to "not enough water". So intake valve is a possibility, but also possibly:


Sensor detecting amount of water cutting off too early (most machines use a sensor of some sort because the fill rate will vary depending on water pressure)
Water filling but not pumping into the spray arms


You should hear water filling when you start a cycle. As soon as the water stops filling, open the dishwasher and you should find a few inches of water sitting in the bottom. Close the dishwasher and open it a minute later and you should find evidence of water having splashed around from the spray arms. If you don't see much water - intake valve or sensor. If you see a lot of water in the bottom but no evidence that it has been sprayed around then a bad pump or valve to the spray arms.