You need to kinda take a look around w/a flashlight. You didn't mention if the floor of your crawl was poured concrete or dirt. You didn't mention how high it was. You didn't mention if it's vented. And you didn't mention where you live. All this would help.
As for the flooring, it's gotta be replaced since the damage is done. Also, can you tell 'us' what you have for flooring UNDER the linoleum?
Jay J -Moderator
Again, for starters, the existing flooring has to go. If the subfloor is rotted, it must go too. DON'T skimp on material - It isn't worth it. If the floor joists are rotted, they either should be replaced or 'sistered' (but don't sister the new joiss butt-up against the old ones. The rot may be xfered ...)
Now, get some 6-mil thick plastic and lay it on top of the dirt crawl. Then, 'weigh' the ends down with pressure treated wood or bricks or gravel or whatever you can to keep it in place. Don't use anything that will rot (as you already know what can happen.) Any moisture coming up from the dirt will get 'trapped' beneath the plastic and simply get reabsorbed. HOWEVER, if you get water on TOP of the plastic from some other 'source', that needs to be fixed. In the next heavy rainstorm, (watch out for lightening), and put on your boots and raincoat and grab an umbrella and survey the ENTIRE perimeter of the house, UP and on the ground. BOTH. Make sure your gutters aren't leaking, or over-flowing. Make sure you have gutters wherever there's water running off the roof-line. Make sure water is coming OUT your downspouts and being 'dumped' at LEAST 3' from the foundation. Make sure no water is pooling near the foundation, and that your landscape around the foundation is sloping AWAY from the house; not towards it.
Fixing/Addressing these types of 'things' solve almost 90% of crawl, basement, and foundation problems having to do with water.
As for the adhesive, I don't think it was the problem. It sounds like the sub-floor swelled due to excess moisture. IF your joists and sub-floor are OK, you'll want to lay 1/4" EXTERIOR grade plywood on the floor for whatever new flooring you'll be installing. (Exterior-grade is more resiliant to moisture BUT not the answer-all.) I wouldn't install any vapor barrier because you'll end up possibly trapping moisture UNDER your floor. ANd that will be bad news. The 6-mill plastic will help dramatically as will the 'outdoor' fixes I mentioned.
Do understand I can't see it from here. My best to ya and hope this helps.
Jay J -Moderator
PS: Don't block your vents.
If the insulation has been damp throughout, that's probably a humidity problem in the crawl space. If only a certain spot is wet, that indicates a localized problem - maybe from rain, leaks, or whatever.