Cannot connect to internet with wireless rou

Hello,
After an ice storm I was no longer able to wirelessly access the internet with my dell laptop. I have tried everything, even bought a new wireless router. Still cannont connect. I can connect if I am plugged into my modem. My computer connection status states that I am connected to the wireless router and the connection is very strong. I am not computer savy to say the least. I have spent HOURS trying to figure this out and any help would be very much appreciated. Please & thank you.