I was hoping ~
When stated after the event has occurred/not occured, it implies something (slightly) expected and pleasent came true/ the opposite came true. The expectation doesn't have to be something you were 100% certain of, it could be more like 60% (I think it is possible, but I dont know for sure). Tone of voice and emphasis will tell you which way:
I was hoping he'd pick me... (he picked another person)
I was hoping you'd buy a large pizza... (they bought a small or medium)
A dissapointed voice means that the hope didnt happen. If any words are emphasized, they are the relevant part of the wish.
I was hoping you say that!
I was hoping he'd be here.
If the tone is happy, it means the wish came true.
Note that in the above, the statement was made after the event happened or the opposite happened. If stated before the event, then the speaker is expressing their desires. It can sometimes also be a request, but it feels a little demanding.
I was hoping you would take a look at my computer
A more polite version of all three of these is the "could" version.
Because "could" is a form of "can", it feels like the situation is responsible, not the people.
I was hoping he could make it to the party... (but he did not make it, maybe he was busy with work)
Just as before, the speaker is expressing dissapointment, but is explicitly not blaming anyone.
I was hoping you could eat with us (as they are all at dinner together)
This expresses joy, but makes it seem like they were doing you a favour. It's an indirect way to say thank you.
I was hoping you could help me with my homework
This is a polite request.
Anyways, for the non-requests versions, you can change the tense from simple present to present perfect (notice -> have noticed) and it means basically the same thing. But it adds the nuance that the wish coming true or not has some significance to the present.
I was hoping you would have been home (but since you are not, you will miss Game of Thrones)
I was hoping you'd have known the answer (and because you did, you were able to tell the answer to me, yay!)
A few days back, the toy broke.
To emphasize the event.
Usually implying that it had broken on its own.
Sometimes just used to tell the story of what had happened after.
A few days back, the toy was broken by someone, somehow.
To emphasize the event.
Probably because you want to place blame.
A few days back, the toy was broken.
To emphasize the state of the toy.
As the listener, I would generally expect the follow-up to be, "But it's not broken now" right after the above sentence.
A few days back, the toy had been broken.
To emphasize the state of the toy again.
However, this time, as the listener, I'm left in suspense about the state of the toy now. So my follow-up now would now, "And now? Is the toy still broken now?"
The reason you're having trouble is because you should use passive voice here, not "got."
Hopefully, this also helps you hear the difference between having used the simple past and past perfect.
Best Answer
These sentences are perfectly grammatical, but they're confusing. You've asked several questions in the past about how much past simple can imply that an action if finished (or can't). Regardless of what was discussed there, one conclusion should be that this implication is only vaguely made, and relies on context to become clear. Another thing to note is that, without any extra context, negating the verb tends to make the opposite implication.
Because of this, it's a little confusing to both say that you "were doing" something and "didn't do it." And the best way to resolve confusion is to use words that actually make the meaning clear: