Modems have changed quite a bit over the years.  Once bulky external accessories or internal cards in your computer they now can be small dongle devices that are powered by your USB port.  No matter which type they are the first and most basic troubleshooting technique is to remove power to the device somehow.  This might require powering your computer off altogether which might be a good idea anyway.  However you are able to accomplish we suggest that power to your device be removed for at least 30 seconds, re-applied and then you can try your connection again.  

While this might sound basic this fixes the majority of modem connectivity issues where the connection was previously working and suddenly is not.  Below are some links that might help if this doesn't work.