My new canary is puffed up and not singing. Is it sick or stressed?

Thanks for your question about Hazlet, and thank you for the photos - they are very helpful. You are correct in that Hazlet is more fluffed than a normal canary should be. You are also correct that this can be a sign of illness (it is part of what we call the "sick bird posture" - this also includes sitting low on the perches or sitting on the ground, closing the eyes, tucking the head, faster breathing). It can also be a sign of stress, or being cold as well. I would recommend that you evaluate where the cage is located - is it near a window, near an outside wall, or near a door? Is the temperature in your house 70F or below - if so, I would recommend increasing the temperature. Now that it has been two days since you posted (I apologize for the delay, by the way), if this has continued and the temperatures and cage location are appropriate, it may be time for a veterinary visit. Often it can take a few days for a bird to get comfortable in their new environment, but if it is still going on now, I would recommend taking him in to see a veterinarian.
They can perform a physical examination, and depending on the findings, may have treatment recommendations for you. They can also evaluate the husbandry/care/diet for Hazlet and may make recommendations that are tailored to you and to him.
I hope that gives you a place to start, and thanks for using Petco Pet Education Center, formerly Petcoach.