2001 Chrysler Town and Country trouble starting

This has been an ongoing problem since april. My van won't start right away. I turn the key and it cranks but doesn't start. Sometimes we have to do it over and over again. Sometimes when it seems like it's gonna start we push the gas pedal a little bit then it starts but sometimes it doesn't. A couple times we've gotten stuck cause the battery dies after trying to start it so much. When it starts it sometimes sounds like it's gonna shut off but we push the gas pedal and sometimes we hear something like popping noises like there is air in there. Now there is a tube that goes into a black box behind where the battery sits I have no clue what it's for. But when I followed it it goes to a joint with two other hoses and one of those hoses goes to the engine. We've replaced air intake valve and I believe sensor cleaned the battery terminals. The terminals and cables have corrosion. Can it be the cables needing replacement? And what is the hose that goes to the black compartment behind battery for?