Wireless internet connected but no internet?

My computer(if this helps)

Is an HP, runnning windows 7.

My internet just randomly shut off one night and won't work. The router is located in our basement so sometimes things get wet, but i'm not sure. I tried reseting the router several times, but no luck. My computer says that it is connected to our wireless internet, but there's no access..? Also, the bill has been paid so I know that's not the reason.

Is there anything else I could do? I pretty much tried everything, even the troubleshoot which told me that theyre was something wrong with my router. But I connected it and all the lights are on. So any suggestions?