Which one is equal to "going hungry"?

'Went hungry' is poor grammar. Hunger is a slow sensation caused when previously eaten food digests and the body needs more. Therefore you can 'become' hungry. It is unusual to suddenly become hungry. So in 'A':-

'Last night I began to feel hungry and grabbed a sandwich to alleviate it.'

B

'Last night, I felt hungry and stayed that way for hours.'

You would not say 'went hungry for hours'.

once in a fortnight i fast - i go hungry,

take only water &1 cup coffee during the whole day.

For this, the better option would be 'B'. The word 'went' has no bearing on the amount of time the person was without food, it simply means that the person did not get any food. The word 'hours' would be the word that would tell how long the person was without food.

No one says "went hungry." You can feel hungry or become hungry. "Going hungry" means going without food for long periods of time.

Too many children in the US go hungry for days at a time because their parents can't afford food.

I was hungry all day yesterday because I didn't have time to eat. 

Last night I was suddenly hungry and grabbed a sandwich. 

Last night I was hungry and was hungry all night,

Or last night I was hungry and went without food all night. 

Went is the past tense of go.

I go to the store hungry, 

Last night I went to the store hungry.

I went hungry to the store - sounds odd to me. 

Get the grammar gurus to weight  in on this.

(A) is definitely WRONG.  The (B) isn't great either, but it's much closer to the usual meaning.  "Going hungry" usually means being without food for a long time, and unable to correct the situation.