My husband is a carpenter and we've been married 43 yrs. We've lived in numerous homes from brand new to 25 yrs. old. It would be more unusual if you did NOT have any squeaky floors. Most houses do or develop them. The floor joists are probably not glued, but nailed. However, boards do eventually bend or warp with humidity and/or age. In those areas where no nails were originally needed, it may become necessary to nail the floor boards to the floor joists in the squeaky places.
If your basement is unfinished it is always better and easier to fix the problem from the basement ceiling area. If the ceiling in the basement is finished and is drop ceiling tiles you can remove them in the squeaky areas to nail the floor boards to the floor joists. If the ceiling is sheetrock and textured (finished) you can cut small sections out of the ceiling as long as you know exactly where the squeak is coming from (it may take 2 people, one to walk the floor above and one to locate and fix the problem). You can either patch & retexture to match the rest of the ceiling (NOT an easy job) or you can hire someone to come in to do it. The entire ceiling may need to be painted and retextured after the patching so that everything matches.
Another alternative is to narrow down as accurately as possible where the squeak is coming from and cut out (use a very sharp box knife) only a small area of the carpet so that you can nail the floorboard to the joists below. You should be able to see where other nails have been lined up so that you know where the floor joists are located. It does no good to drive nails in the floor if there's a squeak if there isn't anything below to attach the nail to (i.e. floor joists). Depending on the style and age of carpet, you may be able to successfully glue the patch back into place without it showing. This is easier to do with shag carpets.
Bottom line is I would get an estimate of costs to remove the entire carpet and put it back down (same company should do both) AND another estimate of what it would cost to patch or repair your basement ceiling if it is already finished.
I hope this helps. Good luck.