Short answer: You can't, not reliably. You can unplug gateway and disconnect the coax for upwards of 7 days, but there's no guarantee you won't get the same IP address again when you reconnect.
Long answer: This gateway is very short on features and had many "issues". This is one, you have no control of the gateway's WAN MAC address that's exposed to the modem function, hence you have no way to force an IP change. Of course, there's no reason to do this (legitimate anyway), so it's no big deal. If you want you can have the gateway put into bridge mode (call 800-363-2416) and get your own router. I recommend this anyway for many other reasons since these gateways are pure junk, but since your new router has a different WAN MAC address, the side effect is that you get a new IP address.
Changing the PC's MAC address is meaningless unless THAT is the MAC exposed directly to the cable modem. Comcast assigns IP addresses to exposed MAC addresses, so different MAC addresses get different IP's. The same MAC is usually assigned the same IP address each and every time, which is why your IP address stays the same for long periods of time even though techinically it's dynamic and each lease only lasts at most 7 days. Unless your exposed MAC address changes (ie the WAN interface on your router), you almost always get the same IP address. And the MAC addresses of all interfaces BEHIND the router are meaningless in this process as they are hidden behind the router's NAT layer.