New battery after driving for a while will not restart

YOU MAY WANT TO CHECK UR STARTER OUT IT MAY HAVE BAD WINDINGS

Battery is not holding a charge great enough to start the engine, acts like it is dead. Get a new battery would be my first step.

Check the engine ground cable.

test ignition coil resistance

Sounds like your starter is the problem. I must be pulling a lot of amps to kill your new battery.

bad power wires

CHECK THE MAIN FUSES, ON THE FRONT,, AND THE BATTERY CABLE.... YOU CAN REQUEST A SERVICE REPAIR MANUAL FOR FREE AT BESTDIRECTORYSOLUTIONS.COM

A dead battery would have given you problems starting before anything else. (unless all you did was recharge it, then anything goes.)
If battery is new , I recommend you take the vehicle to a repair shop this way they can pull the tires off and see whats holding the brakeswhile they are applied.

When you replaced the battery, you erased the computer memory. Drive it for awhile until the computer learns how to run again, it will be fine.

try getting a boost for your car.... the battery may be failing. it doesn't take alot of power to turn on the lights... but a huge drain on the battery to start it. if it will not start with a boost i could very well be that the starter has failed. as you attempt to start it... have someone tap the starter with a hammer. if it starts... replace the starter.... if it starts normally with a boost you likely need a new battery