When we got Casey, it was hell on Earth while we tried to crate train her. I can say now, happily, that she loves her crate and puts herself to bed and in for naps most days.
Have you read up on the proper way to crate train? The biggest problem is that most people do it incorrectly. Run a Google search and find a reputable website (vet or handler based, hopefully) and see if you're doing everything correctly. Otherwise, I would say invest in a book from a bookstore.
With Casey, we found that putting a blanket over her crate worked, too. Initially, she didn't like it either. She would find the smallest hole to peep through and would howl through it. One of the biggest things with crate training is holding out and seeing them through it. They will, eventually, come to like their crate if you're doing it properly.
The other suggestion of
exercise, exercise, exercise, was one of the ones on my list, too. Depending on the type of breed, some dogs need a lot of exericse. Casey is/was one of them. We will take her to play fetch/soccer and
then swimming just to run her ragged. If she doesn't get her exercise, look out. No ne can sit quietly and watch TV. Find something that fits your routine/schedule and get into a routine. The dog has probably lacked a schedule, routine, and structure for quite awhile. You've got to get them back into it. It's like having a puppy when you're trying to figure everything out. We kept a diary that just tracked when she ate, when she peed and pooped, how much exercise she got, how much she ate, etc. It will help you establish the dog's routine and will make it easier for you to work their schedule into your schedule. We know that if Casey doesn't poop at 6:40am, there's something wrong.
My mom was having a lot of trouble with her two dogs when she remarried and introduced a third dog into the house. They were all male dogs, so they would pee one right on top of the other. Not good. While I visited one time, I crate trained them. They were 5. The biggest thing with non-previously trained dogs is to be with them right there and put them in their crates. With them, I would pull their crates into the living room and put them in the crates. I'd hunker in and watch a movie or read a book. Initially, they'd be in there for a half hour or so every other hour. Then a half hour every hour. Then 45 minutes. Then an hour with a half hour break between.
Slowly move the crate out of the family room/room you're spending time in and towards where they will be living once crate trained (see below, too). It taught them that the crates were their dens... something most animals need and want. It also helped them realize that just because they were being crated didn't mean people were leaving for several hours. Have you established a going-out-the-door routine with the dog? If not, you need to- bathroom, crate, treat, whatever it may be. Do that routine while you're training so that they get used to this is what happens before going in the crate and not necessarily as you go out the door (both, really).
Is there something funny in the crate with your dog? Does it smell like something else? Another animals bed linens? Have you washed it since purchasing it? You need to establish that it's their place ad invest in or recycle a blanket or towel and let them claim it as theirs. Casey will actually mumble about the cats being in her crate of they decide that's a cozy place to call home.
She also sounds like she gets bored. Hopefully you can start exercising her/him to a point that they look at the crate a realx/sleep time. Until then, keep them occupied. Do you have one of the breeds that needs to be doing something constantly or gets bored easily (Collies come to mind)? If so, you're going to have to find a remedy that works for your specific furbaby. Kongs? Rawhide? Durable chew toy?
Your crate should be somewhat in the middle of your home so that the dog doesn't feel like they're being ostracized from the family. Casey's is in a nook right outside the kitchen. Right now, DH is making breakfast and I am nearby on the computer. Where is she? In her crate. This will help tremendously as you put them in for a short period of time and work your way up in minutes and away in distance.
Personally, and I haven't met the dog... she sounds like she's having anxiety about being left alone. You said shelter and you never, ever know what's happened to them. You may be trying to fix something that runs far deeper than exercise and whatnot. You may have to heal the inside first. Bless you for choosing a shelter animal though.
Lastly... is the crate big enough? I wonder becuase you said the dog was able to do something to it. They
must have enough room to stand up, sit down, and turn around in it with clearance above their head and hunches (by law). If they are able to fully lay down and spread out, it will only help.
Good luck! Always here to help and please PM me if you need something!
ETA: For the most part, we still crate her at night. That was the big one we had trouble with Casey becuase she would howl all night long. We ignored her and didn't give her attention at all. That's what they want- attention- whether it be positive or negative. We got into a habit of getting everything set and ready for bed before putting her into her crate.We'd be in PJs and have everything taken care of for the next morning (cell phone charging, teeth brushed, alarms set, lights out, bed turned down, etc). We'd take her out for her last trip and then put her in the crate. We'd sit with her there in the kitchn until she fell asleep. Then, becuase everything was ready, all we had to do was get into bed. If we so much as flipped a light, she'd wake up and cause a raucous. It only took about 2 weeks of this. Looking back at it now, I think she was scared of the new home and noises at night. She's always been a dog that's wants to be with people and I know the night separation bugged her. I will admit that when she woke us up in the middle of the night (well, woke me up since DH was gone with the military a lot), it was a PIA the sit there with her and do homework at 3:00 in the morning, but in the end, she settled it and went to bed nicely.
Good Luck!
(walk him first and then do training!!!)
Cherry & Maisy 
