I am not sure why most people are afraid to deal with carpeting. I come accross this all to often. What needs to be done is simple. Pull back the carpeting and the padding fix the squeeks with some screws. And put the carpeting back with a power streacher. ( rented at home depot for about 20 bucks a day.) This term power streacher is not a correct one as there is not power used. It is just a very basic tool that expands to fit the room and push off of the oppisite wall. Go along your wall and streach in the carpet. Then tuck in under the baseboards.
Ok .. now answer me this. Why do you have a subfloor in your basement? I am from Indiana, and have never seen this in many , many years.
Thanks