As long as you know the baby is not ill, it appears he might be having a tough time being away from his previous owner. Since he stops crying when he is held, they might have held him a lot.
Just be patient (get some ear plugs) and you may need to let him cry a bit. It is like bringing a puppy home, they cry a little (at night) because of the new environment and missing their litter mates. Be patient, it will be worth it.
I have a little one that is used to waking up at 3am (like clockwork) and doing her business, after she goes outside we curl up on the couch and watch tv. Just this morning I was tired so hubby took her out and put her back in the pen to go to sleep. She wasn't having that and cried until I got up. I am a mush mess when she is sad.
