If you just reformatted your computer it's likely that it won't get to the Internet until you install/update the NIC/Ethernet drivers.
If you have the Dell system/driver disc that came with it use that.
Otherwise I'd recommend you use the laptop that works to go to Dell's website, look up the drivers for your computer model and download the Network/NIC/Ethernet drivers.
Put that on a USB thumb drive and install it.
After that you may need to restart depending, and then go about updating/installing all your need drivers/software/etc.