your desktop works so its not a router problem ,is the laptos wifi turned on,most laptops have a on\off buttor or key combonation to turn the wifi on ,,not knowing what brand and model the laptop is its harder to help .
Has the laptop previously been able to connect to the router? Who is your ISP? I had a similar issue with my Time Warner Cable wifi modem/router (Arris TG862) when TWC upgrade services in the area. For some reason it disabled all devices connected to the router and after a call to TWC the solution was to have them reset my cable access (a simple, 10 second procedure) and then reconnect all devices. Annoying but easily fixed.