1999 Taurus feels like it's slipping into neutral while driving

I bought a 1999 Ford Taurus "used" from a car dealer. The problem:
 
I can be driving my car and it feels like  I put my car in neutral. When this happens my speedometer drops to zero and no matter how much gas I give it, it feels like the gear is in neutral and won't go anywhere.  Actually that's when it does happen. It's like my speedometer gets stuck or something. If I keep giving it the gas it finally unsticks and goes back to normal. I mainly have this problem when I'm stopped and pulling out.
 
Anyone out there have any idea what's causing this? My DH has racked his brain trying to figure it out. TIA