Are these sentences correct:
1-I closed my mailbox with three messages unopened.
2-I closed my mailbox, with three messages unopened.
3-He kicked me with my hands tied in my back.
4-He kicked me, with my hands tied in my back.
When he kicked me, I had my hands tied behind my back.
2 - Yes, the comma is OK and helps to avoid the confusion I mentioned in 1.
With both 1 and 2, I might add "still" before "unopened".
3 - No. It sounds like "He kicked me with my hands" (and that the rest of the sentence is just extra information).
4 - Yes. Having said that, I would probably not word it that way. I would have said "I had my hands tied behind my back when he kicked me" or your alternative.
Remember - correct capitalisation, punctuation and spacing make posts much easier to read.