Is your PC the only device in your home ? (The only device on your home-LAN, except the router of course). If not, try (for a few hours) with everything disconnected, except your PC.
If it re-occurs, with only your PC connected, then the problem is either:
1) your PC
2) your router
3) your ISP
You can test 1) by attaching another device, and shutting down your PC. A laptop (from work), or a tablet, anything that can do pings. Do you see the same problems with another device ? Yes -> problem is your router or your ISP, No -> problem is your PC.
Do you see the problem with the pings when pinging through your router, to something on the Internet ? Or do you also see the problem when pinging to your router itself ?
Do a traceroute (tracert -d in a dosbox) to somewhere on the Internet. The first IP address you see is the IP address of your homerouter. The second you see is the IP address of your ISP's cable router. When you ping those 2 IP addresses, do you see the problem every half hour too ?
You need to be systematic to find the exact location of the problem. Only then can you find the exact cause of the problem. This is basic trouble-shooting strategy.
If you don't trust the router, you can try and find a forum that discusses the type or brand of routers. The vendor (Motorola) might have one. Or your ISP might have a forum for its customers. Or there might be a newsgroup. If indeed it's a generic flaw in your router, I am sure others have ran into it already.
You might also try to upgrade the firmware of your router to the latest version. Won't hurt.
Basic steps. Otherwise it will be just wild guessing.