Did you install or enable the https security certificate when you installed Replay Media Catcher? RMC5 accomplishes downloading of HTTPS content, such as at https://www.youtube.com, by creating a proxy. When monitoring for internet downloads is turned on, the proxy setting is activated. If RMC5 is unexpectedly shutdown, the proxy setting might get left on and interfere with internet communications at the next boot cycle. You can go to Control Panel\Network and Internet\Internet Options, select the Connections tab, and click the "LAN settings" button to turn off the proxy setting. This should re-enable the internet connection. Turning on and off monitoring will toggle this setting, and it sounds like yours got stuck in one state or other.

If you are not particularly interested in YouTube content, you can turn off the SSL scanning feature (Settings->Internet->HTTP Adv). This will stop the proxy activation. You can still download from YouTube if you use the HTTP connection as opposed to HTTPS. However, more and more customers are finding that their browsers are being forced to https://www.youtube.com, hence the creation of the SSL certificate and proxy system.