"would" is used to express something that doesn't actually happen.
There's always the hanging question "why isn't it happening" when you use "would" and that's why you need another phrase to qualify it, whether in the same sentence or from context established from a previous sentence.
- I would go, but I'm feeling sick.
I'm not going, the reason why - I'm feeling sick.
I was at the park at some time in the past, and I'm implying I'm not there anymore by saying this.
- I would have gone to the park.
Say just this to someone and the other person is going to immediately ask "Why did you not go to the park?"
- I would have gone to the park, if I wasn't feeling sick.
I wanted to be at the park at some time in the past but that didn't happen, the reason why that did not happen is because I was feeling sick.
We can't tell from this sentence alone if she is sick now, but it's a possibility. If we want to make sure we contain everything in the past, we can specify the time "I would have gone to the park, if I wasn't feeling sick yesterday" or "I would have gone to the park yesterday, if I wasn't feeling sick."
- I would go to the park, if I wasn't feeling sick
I want to go to the park now (or soon), the reason why that will not happen is because I am feeling sick.
A conversation might go like this:
A: How were you feeling yesterday?
B: Not very well.
A: Too bad. I went to the park yesterday.
B: I would have gone.
A: You should have, it was fun.
A already knows why B didn't go, so B could get away with not saying why in that sentence.