It all depends on the state.
At common law, regardless of whether or not you had a key, if you entered with the intent to commit a crime and used the slightest bit of force, including literally pushing an open door or even an INTERIOR door open, you could be found guilty of burglary.
However, one of those quirks of common law is that it had to be at night.
Regardless, you could be charged with Larceny which (i) requires a taking and (ii) carrying away (the slightest movement counts) (iii) the personal property of another (iv) without his consent (v) with the intent to deprive owner permanently of their property... although permanently doesn't really mean permanently
Remember, taking property in the belief that it is yours or that you have some right to it is NOT common law larceny. It can be other things, though.
However, if you got that key under false pretenses, you could be charged with exactly that; false pretenses.
Regardless, you're not off the hook just because someone gave you a key. You're not even off the hook if someone hands you the thing you're stealing from them.