You might be losing DNS service.
The internet radio already has a connecetion to the source site so it does not need to resolve the IP address. You browser on the other hand can't ressolve the IP address of the site you are looking for so it says it can't find it.
Rebooting the router and the computer probably will not help.
You can go to the network set up and put in your own DNS servers and use them in place of your ADSL provider's supplied servers. Try putting in 128.9.0.107 or 198.41.0.4
Good Luck!
Bill