Hello, Amir. While I do not have direct experience with boat carpets, I do have extensive experience with the old "musty" smell. The only way to really get rid of it is to find the source of the moisture [any kind] and get rid of it. Moisture can be found in many different areas, especially in such an old structure and can be caused by something as small as condensation on the windows [usually at night] leaking into the cracks of the walls and constantly or occasionally wetting the insulation. Anything that is currently moist will have to be either removed or dried and treated and whatever is causing moisture to begin with must be eliminated.
You can try a couple of things first, if nothing stands out as an obvious source of moisture. Try laying out large, flat cookie pans with spread out activated charcoal. The more the charcoal is spread out, the better. You don't want it in piles on the pans as this increases the surface areas of odor absorption. If you don't have activated charcoal, you can try the same thing with regular unused charcoal, unused coffee grounds or kitty litter with baking soda mixed in. Another thing you can try in a room intended for storing things is to paint that room using a hefty amount of vanilla flavoring mixed in with the paint [please note, this will alter the color of the paint].
Bleach does wonders on carpets that you don't care what they look like but with some carpets, it will damage the under layer, glue or possibly both. Some molds will actually feed off of the bleach so I
usually do not recommend this approach. Most of the time, I will advise to get rid of it completely and start off with new padding/carpet only after getting rid of the moisture issue(s) and coating the substrate with a layer of oil-based Kilz. You might try to get rid of or remove anything that attracts moisture as well. For example, old drapes, comforters, boxes of clothes, books, drop down ceiling tiles, etc.. If it's bad enough, some folks do a rip out and hire a dry ice blasting company. In your case, it might be cheaper to just build another outbuilding, using the existing plumbing and electrical.
Anything that you store in there can be preserved if stored correctly.....even without doing anything to the trailer itself. A good example would be to place small items in Ziplock freezer bags and placing them inside a "Goodwill find" Tupperware container or one that you just have laying around the house, unused. Place multiple items like these inside a Rubbermaid container surrounded by charcoal and secure the lid.
Sam's Club also has a product called Odoban. While it isn't as strong as some of the industrial odor eliminators, it does a good job and is a very good value.
http://www.samsclub.com/sams/odoban..._18492716&cpncode=30-199854167-2&pid=CSE_Bing It also doesn't cost as much as an industrial odor eliminator. Some of those can be upwards of 18-42 dollars a bottle for 1/5 the size container. Odoban works rather good if continually used and at the cost, it's kind of a no brainer. I just use mine full strength and over the course of a week or two of continual use, it smells like odoban and not the smell you were trying to not smell.
Another trick you can do is to constantly use vanilla flavoring or Odoban on a piece or pieces of fabric softener at the HVAC filters.
With all that said, the best way to get rid of the old musty smell is to remove what causes, absorbs or creates the smell to begin with and look for any and all sources of moisture and eliminate them all. At that point, the recovery to good smell can begin to become permanent and not just a mask.
Tom