Modals

I saw a question on the forum and wanted to expand it to clarify some major issues on using modals.

How to use modals should, could and would for the past?

I know that "should" has no meaning referring to the past tense, but what about "could" and "would". They are according to dictionaries respectively the past simple of "can" and "will", but seemingly we are experiencing them being used not completely that way.

Look upon this sentence please:

I would go to the meeting but I had to study.

The correct form is said to be "I would have gone to the meeting but I had to study", but what is the reason? If I want to know something I shall I be accustomed to its reason.

What about these, please toy with the following too:

He could go to school but he was impeded to that.

Does the modal "could" not having any meaning of the past —just like "should" in the next sentence?

I should attend the conference but I arrived late.

Here, I'm convinced that since "should" cannot solely refer to the past we should use "should have attended" instead.

Do we have any rule saying that no past modal verb (might, could, would, should) can solely (as above) be used for the past tense?