If I had run the race, I would feel accomplished.
If I had run the race, I would feel have felt accomplished.
Both of these are correct.
In the first case, the speaker is saying that had they run, they would currently feel accomplished. In the second case, the speaker is saying that if they had run the race, they would have felt accomplished in the past.
They are very close in meaning, but have a different time sense in the consequent. If you wanted to to say something more about the past time frame in the next sentence, you would need to use the second and not the first: "If I had run the race, I would feel have felt accomplished. Instead, I was filled with a sense of incompetence."
Next,
If I had ran the race, I would feel accomplished.
If I were to run the race, I would feel accomplished.
Change "had ran" to had run in the first. Otherwise, they are both correct.
The time sense of the first is identical to the time sense of the first above - if the speaker had run in the past, they would currently feel accomplished.
In the second, the speaker is saying that if they run the race in the future, they expect to feel accomplished in the future, after running.