I am sorry to that you are in this situation. I am, too, an F1 student, and I understand these kind of paperwork issues can be very worrisome.
Since you haven't lost your old passport or your old visa, I would suggest just wait. Getting a new visa takes a while, even if you explain your urgent situation. As cruel as this sounds, the US government doesn't really give a crap about whether you can start school on time.
I had a friend who forgot to bring her I-20 when she entered the States, and after going through secondary inspection, she was allowed in. When it comes to visa though, I have no idea.
I highly doubt the USCBP officer will admit you without your F1 visa. And if you are flying, chances are you won't even be able to roll that dice. Pretty much all airport staff will check your US visa when you get your boarding pass. This is because if you get deported, they have to fly you back for free and they get fined by the US government. In fact, many airports now check both the US visa as well as the original I-20 for all those flying on F1.
If you are driving, I don't know what will happen. You can try, but get ready to be denied entry. Also keep in mind a denied entry doesn't play well next time you apply for a US visa, or any visa or immigration document in any country for that matter (because they ask for those information).
In a word, just wait. Since your visa is already on the way to you, it shouldn't take long. Finally, I hope that you could get your visa soon and be on your way back to the States. Best of luck!