Both of the below sentences or surely correct. Could a native speaker (or any non-native but good English speaking person) tell me when (any context) we can use 1) and 2)? I know present perfect relates to the past and any action it describes presumably ends at the time of speaking. I would just like to feel the usage context better.

thank you in advance,

1. With all the work I've had to do, I've not got around to ringing.

2. With all the work I had to do, I did not get around to ringing.
Here, the present perfect brings more immediacy to the speaker's complaint. The present perfect in the main clause also suggests more clearly that he may yet ring. The facts the two sentences reveal are identical, however: he did a lot of work, and he didn't ring.

Your two sentences tell the same story, but from two different points of view.
The first is a present-viewpoint sentence; the second, a past-viewpoint sentence.

At this very moment I have still not rung because I have had so much work to do during this most recent time period. (The situation described here still exists at the moment of speaking.)
Some time ago I did not ring because I had so much work to do during that time period. (The situation described here no longer exists. It is a situation which existed in the past.)

If we construe "some time ago" in the second sentence as "some very short time ago", it approaches the meaning of the first sentence more closely. Exactly how long ago is not something which is specified by the past tense itself.