I do this for a living. Knock the old one apart and take it out by sections small enough that you can handle. It'll be messy, but manageable.
And depending on what you order, it might be a knock down or packaged boiler. Knock downs have to be assembled on site. Packaged units come assembled and you have to rig it into the basement. All depends on access.
I did 4 boilers last year (Burnham V1120's), each one weighed 8000 pounds. Three of the four I had ordered as knock downs, one packaged. Two knock downs all went UP a flight of stairs, one section at a time, the other knock down went through a 36 inch wide door, one section at a time. I got away the 4th being packaged because I had great forklift access. The units I demo'd all came out one section at a time.