Check other computers
The next step is to figure out whether it's your Chromebook or the wireless network itself causing problems. Try to connect another device to the wireless network. If that device can use the web when connected to Wi-Fi, the problem is with your Chromebook. If not, the router may be at fault.
Test the wired network
If none of your other devices can connect to the Internet through Wi-Fi, there may be some other problem with your router. To test this, you'll have to try connecting your Chromebook--or another computer--to the router the old-fashioned way: with an ethernet cable.
Unfortunately, most Chromebooks don't have an ethernet port. If you've made the commitment to use a Chromebook as your regular machine, you should probably invest in a $13 USB-to-ethernet adapter.
If you can connect to the Web through the ethernet cable, you've discovered that it's definitely the wireless network causing you grief. If not, the router, modem, or your ISP are the likely culprits.
Sign up for CIO Asia eNewsletters.