Upvote:3
It's unusual that they did not cancel your old visa when you went to apply for the new visa. Usually, when you apply for a new US visa, especially if it's the same kind of visa as in this case, they cancel the old US visa as the first thing, regardless of whether or not you are approved for the new visa. Check your existing visa to see if it has something like CWOP (cancelled without prejudice) written over it.
If they indeed did not cancel your existing B2 visa, then yes, you can use it to try to enter the US on any day on or before the expiration date. Note that a foreigner (especially a visitor) can always be denied entry. The immigration officers at entry also make a determination of immigrant intent, and will deny you entry if you cannot convince them you have no immigrant intent. And the fact that a consulate so recently denied you a visa for immigrant intent (INA 214(b)) could very well affect the immigration officer's determination.