As for squeaky floors ... are they hardwood? Carpetting? It's possible for them to squeak even if the surface is new (either refinished or replaced) if the supports were not reinforced or adjusted. Did these rooms squeak when you first walked through the house? When did you notice the squeaking?
Did you use an attorney with the purchase of this house? If so ... he/she would be the best place to start.
I guess, like everyone else seems to be indicating, I see no obvious recourse. There are many steps put in place to try to prevent this sort of misunderstanding and the key would be how these squeaky floors managed to get past all those checks ... if, at any point, there was some sort of active misinformation or misrepresentation about those floors, then you are more likely to have a case. More so if you have it in writing.
Once inspected and any problems are sorted out you are buying the home as is. No matter what you find afterwards even if it shows that the home was blatantly mis-represented you are stuck with it.
Most important persons in this process are your inspector and your lawyer (not your realtor)
"Fully" is a subjective word and one that will be hard to uphold in the court of law. I just sold a renovated home and there were many things that were not done. We allowed the buyer a home inspection and they understood that if it was completely new the home would have been 100K more. I would just bring in a contractor to fastened the floors and you should eliminate the squeeking. Best
Rennovated does not mean everything is brand new. It means the property has been updated. When you did your home inspection it should have been apparent that some items were not brand new. Squeaking floors are not uncommon and they are actually pretty easy to fix http://www.squeakyfloor.com/prodsqueak.html. There is another product called squeak no more. Both cost under $20 and about an hour of your time. I'd try this before I pursued legal recourse.
I tend to agree that "fully renovated" is not a legal term which everyone would automatically agree with. I also agree that squeaky floors would not require an inspector to discover and would have been evident to you and anyone else in the home.
You should seek a legal opinion if you feel there is a good reason, but it doesn't sound like a wining case to me.
I'm sorry you're dealing with this!