The LAN lights are a response to there being a physical connection detected. If they are missing triple check the physical connections between the gateway and your PC. If you're wireless, there won't be any LAN lights lit up. Resetting the modem won't have any impact on this issue. It's a physical thing rather than software.
Is your computer directly plugged into the modem? (Is there anything plugged into ports 1-4 on the back? Should there be?) If yes, check to ensure the ethernet cable is plugged into your PC and see if the network card has any lights lit on it (most do but not all). If no, is anything else plugged into the modem?
Ok, that makes sense. Now if you've reset your modem, that usually clears the wireless settings if you set up your own network name and password. If you just rebooted it or you kept the default network name / password, you should be ok.
Are any of your devices able to connect wirelessly?
Is the Wireless / WLAN light lit up on your gateway?
What type of device / operating system? (PC, tablet, phone etc)
In your device settings, does it show you connected to the correct network?
If it's not connected / was reset and you don't see your own wireless network, check the underside of the modem for the default network name and wireless key.
Usual troubleshooting process would be to connect a computer to the gateway with an ethernet cable. This should give you an internet connection no matter what. If not, you may need to may need to press the reset button on the gateway with a paperclip.
Once you know you have a solid, wired connection to the internet, then you can start to track down the Wireless issues. Log into the gateway using the credentials which came with it (usually on the bottom of the gateway) and go to the Wi-Fi section to confirm the wi-fi login credentials. Make sure these are accurately transferred to a wireless device. you should then be able to confirm you are connected to the gateway by either activity on the wireless device, or on the log screen (first page) of the gateway management page you have logged into on your computer.
Let us know what you learn.