I own a 2004 Ford Explorer. It has a brand new battery, but when you turn the key in the ignition nothing happens. The lights comes on and the radio works but nothing else happens. All the dash board lights comes on. When my husband gets underneath and touch the starter it turns over but still won't start.
This could be a whole lot of things. I'm going to guess that the check engine light is on (and / or On and blinking...)
If so, we're going to need to see the stored OnBoard Diagnostics version 2 (OBDII) codes. The only way to get those on your car is with an OBDII reader. (either via a purchase at your local autoparts store, or online somewhere, or borrow one from a mechanic friend.) In some areas your local autoparts store will read the code for you for free, but obviously that won't work if your car doesn't start.
If there is no check engine light, this sounds like an electrical issue. I'm guessing you've likely got a fuse or solenoid out somewhere. My recommendation there is to check all fuses in the vehicle, both underneath the drivers area of the instrument panel and under the hood... You can find a directory to all fuses in your owners guide.
Another recommendation: Purchase a Haynes or Chilton's service manual for your vehicle. They cost around $30 for your vehicle and its money well spent. In this case they provide a complete wiring diagram, so you can determine which relay or other area of the car could cause this fault. They have a decent 'fault' tree so you can troubleshoot the now start defect in a systemic way.
And what lead you to replace the battery in this car in the first place? Has the car been started even once since the battery has been replaced?