My home is less that two years old. There is a banging sound, that comes out of my baseboards. It seems to happen , after the heat is shut off. My plumber purged the system, but I still have the problem. It is so loud, that it wakes me up at night.

Usually air in the lines will do that or a valve or pump is doing a hard shut off. This is something that needs to be figured out on site. Get a different HVAC company to look at it.

Slab or basement? It is hot water heat correct? (just making sure) Is it only 1 radiator that does this? Is the system zoned?

Unfortunately, I found out that the noise, doesn't come from the pipes. What I am hearing, is the sound that the floor makes, after the heat goes off, and the wood contracts. My plumber checked all of the pipes, and that's what he said. It makes sense, because, after listening to it for at least six months, it sounds like a snapping sound. It only happens, after the heat has been off for a few minutes. But, it always happens the same way. The heat shuts off, and, after about five minutes, the noise starts. I hear a snapping sound, that lasts for quite awhile. What I do know is that it definitely has something to do with the heating system, because it always starts a few minutes after the heat shuts off. What I would like to know, but am really afraid to find out, is that there might be something wrong with the structure of my house. I have a brand new house, but I'm really afraid that something is seriously wrong. I know that houses settle, but, I don't think that this is normal. I would appreciate any comments, or a solution to this problem. Thank you.

Check to be sure all the plastic element sliders are still in place. They insulate and provide a smooth slick surface for expansion and contraction of the baseboard element in the housing.

My plumber checked, and the sliders were in place. He said that he couldn't find what causes those loud sounds. Is it possible that there is a serious problem with my house?

Is it possible that there is a serious problem with my house

NO

Could still be air in the lines no matter how well it is bled.
It could be expansion if the tank was not installed properly.
I suggest giving some other contractor a shot at the repair.

I'm sorry to be such a pain, but what you are saying is that it is possible that it is a plumbing problem. The thing is, is that the original plumber is the son of the plumber who told me that it's the house settling. Again, it is a snapping sound. I hate to bother anyone with this problem, but, I have doubts about everything about my house. I don't know who to trust anymore. It really sounds like a floor settling. Like when you step on the floor of a new house, and the floor makes a creaking, snapping sound. At least. That's what my contactor told me. I don't know anything about what sounds new houses make. I can't say that I trust my contractor. When I had my furniture delivered, one of the delivery men stepped on the floor in one of the bedrooms. It made a really loud snapping sound. The delivery guy said that, it didn't sound good. It made a really loud cracking sound. This is why I don't know what to think. I have a brand new house, but, this can't be a normal problem. I'm sorry if I make it sound confusing. I have lost a lot of sleep, because of this noise. I appreciate anyone's help in this situation.

Contact the local building department in your area for further assistance. They just inspected the home if it is new so they might have a answer. Your flor joist's could be to small or the floor covering (plywood) could have been installed with no clearance. That will make some snap noise when walked on. It could be many other problems also but I have no cure for you here. Noise is about impossible to figure out long distance. It takes a personal visit to the site.