Hi Alex,
Quote:
- "He couldn't conceive of a time" -> the sentence is talking about the past when he was not able to get the feeling of time. The action happened in the past -> Then why the next clause used a conditional "would" when it could use a simple past?
First, let's be clear about the meaning: "he couldn't conceive of" means "he could not possibly imagine" (not "he couldn't get the feeling").
Then, as you identified, the sentence is describing the past.
When we talk about the future from the perspective of the past, we use the conditional ("would"). This is important to know for the GMAT, as it does come up.
For example, a CEO stands in front of the media and says "We
will expand into China in 2019."
Then, a week later, the media report: "At last week's press conference, the CEO announced that the company
would be expanding into China in 2019."
There is nothing hypothetical in this sentence. We use "would" to capture that the CEO was talking about the future in the past.
Does this help clear it up?

I understand that we rewrite "will" into "would" for the future actions stated in the past. However, i still have confusion about this question and let me try to explain my confusion once again.
Meaning: He could not have the feeling of time which means he didnt feel that time is running away or something of that sort when he would have no job?!
Let's go back to that past to rewrite that sentence in present tense. "He cannot conceive of a time when he will have no job" -> I cannot understand this at all. How he cannot get the feeling of time when he is talking about some time in the future when he will be jobless. We dont know if he has the job NOW?! What if when he has a job, he does have the feeling of time. He only cannot get the feeling of time when he is jobless. These two actions must be at the same time period. How are they happening in different points of time?
I am so confused.