Could they be bottomed out? Hope not. Since you can turn them, thats a very big plus. Maybe it's time for some much needed wheel maintenance.
Remove the wheel from the bike and then the tube/tire from the rim. Completely remove a nipple from a spoke. (Can be done with a big screw driver from the outside of the rim) In your case you might need to dedicate a screw driver for just this task by grinding a relief slot in the middle of the blade to straddle the end of the spoke in the nipple.
Completely clean the spoke threads and the nipple threads and run it back on the spoke and see if you can get it to the desired ping. If it does the job, repeat on all spokes.
Do them in a sequence a few at a time to keep the wheel as true as possible, and just bring them back to a good snug. When all are done go through with proper tightening sequence. If you do a search here, there are a bunch of threads on wheel truing. (At my typing limit, sorry) Hope this helps, good luck!