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3rd Gen Ram Tech2002-2008 Rams: This section is for TECHNICAL discussions only, that involve the 2002 through 2008 Rams Rams. For any non-tech discussions, please direct your attention to the "General discussion/NON-tech" sub sections.
I found a section of a manual that lists all the plastics and what parts are made of what. It doesn't mention the HVAC housing specifically, but I didn't spend much time looking.
Pretty sure it's abs, you can make a concoction out of scrap abs and acetone that should work. Go to YouTube and look up abs glue, there are a couple videos on this. I used it on the dash of my Miata and it seems to have worked out well.
JBWeld picture frame hooks to both sides of box, then twist wire around them to hold it together. Or insert two screws into each side, wrap wire. Done.