Is it Cox or my router that is giving me terrible internet?

My family owns a Belkin Wireless Play Router. I often game on PC and when i do, the internet is terribly slow and laggy and randomly will shut down for up to 5 minutes. But when im watching youtube videos, watching live streams, it seems to be fine. My father also has a filter on our internet called Kerio. I think getting a new router would fix the problem, what do you think?