Bicycle Tutor

Hello,
I have a 3 day old road bike that I got for fathers day. I only have about 20 miles on this and today after work I hooked up the Burley and grabbed my 14 month old to try and get a quick 8-10 mile ride in before supper. About 2-1/2 miles into the trek the rear wheel started making a loud pop sound every 10-20 seconds. I looked back and it appeared the the chain was jumping gears. I tried different gears and had the same problems. I decided to turn around as the pops were accompanied by the pedals slipping pretty violently causing my feet to shift in the pedal cage, and the noise was scaring my boy.
About 1/2 mile away from home the chain stopped grabbing all together. I would pedal and the chain would only grab occasionally. I ended up having to walk it home. Any idea what could have caused this? The bike has not been dropped, laid down, gotten wet except for driving though a small patch of sprinklers on a morning ride. I am stumped as to what caused this to happen and wanting to know if this is something that I could fix easily so that I can get back on the road.

It sounds like the freehub (freewheel) has gone faulty.
With the bike at a standstill, turn the pedals and watch the rear gears. If the gears turn without the rear wheel then it's the freehub/freewheel that's gone.
If the bike is from a shop then take it back for a new one.