1986 Chevy Celebrity won't start, attached photo

[Apache47]

What is this valve on top of the engiine, what is it's function ? What are the hoses attached to it ? If they are not working will the engine not start ? I was given this car
by my mother in law, the engine only has 54K on it, but has sat in a garage for over a year. A mechanic changed the oil but it was not driven frequently. I towed the car home
as it was a long drive . The car started up after installing a new battery. It ran fine but a little rough. We had a tuneup performed, plugs, wires, rotor and fuel filter and mass
air flow assembly. After the tune up, frankly the engine seemed to run rougher, but it ran. Last week it just quit in the street and I had to have it towed home. I had a mechanic
come out who changed the fuel pump located in the gas tank. The car will turn over but still not catch and run. The mechanic said that the hose that I have circled in that attached
photo was some type of air hose and the pump that it was attached to underneath the battery was faulty, but he could not tell me what it was called. If this hose is not
working properly, will it prevent the engine from starting and running ? What is this valve coming out of the manifold called and what are the hoses attached to it called and what are their functions ?

Thanks.

 

[zora]

Do you have spark at the plugs?
What is the fuel pressure?
Why isnt the shop that did all the work taking care of the issue?
If the hose that comes off that "valve" goes to the brake booster it should have nothing to do with the no start condition unless there is a crack in the hose.

 

[Chuzz]

My eyesight isn't the greatest, so I'm not sure about that "valve". But it sure just looks like a ported vacuum switch to me and would have no bearing of the car running or not. I'd suggest having a COMPETENT mechanic check it out and not the moron you've been taking it to. He's probably screwed you out of a lot of money you didn't need to spend. It might just be a bad crank or cam position sensor.