WELCOME!!!!! I edited your post to delete the strange sad face fluke thing.
How wonderful of you to bring in this poor banged up bunny. It sounds like he really needs love and patience. He seems to have been through quite a bit, and his reluctance to come out of his cage is no surprise.
You can try to put a treat outside of the door. I know you don't know what he likes just yet, but maybe put some boxes out in front that he would feel safe to go out of his cage to explore and hide in.
Having him get used to you will also help him trust to come out. When you have a free moment just sit by his open cage. Read the paper, work on a laptop, read a book, listen to music, whatever. Just get him used to you being there without expecting anything from him. That will help him begin to feel safe too.
My big white bunny, Jack, is a big scaredy cat, and when we moved, it took him two weeks to venture out of his pen, and then another two weeks to venture out of the bunny room and into the rest of the house (and that only happened because I finally picked him up and carried him since it had been over a month total) I wouldn't advise doing that just yet with your guy as he really needs the chance to feel safe and get used to you.
You can see Jack's drama and what we did to solve his "boycott" on venturing out in his blog:
The blog starts with his most recent event, so you may have to go back a few blogs to see the beginning of the "moving" saga.