I use this method often. It takes just about the same amount of time to power up and cycle your cable modem. I've never had any luck with web-based proxying; it seems whatever site I find, they want you to buy something.
ETA: Cable modem users can't just turn the modem on and off; we have a static IP that won't change while the MAC address for the modem remains the same. I used to have a DSL line, and yeah, all you had to do was disconnect, then reconnect and you'd have a new IP. The method described above changes the MAC address of the modem (temporarily), so that when you cycle the modem, your ISP believes you're connecting with a completely different piece of equipment, so it gives you a new IP.
There a lot of steps above, but really it's just using the MAC address spoofer (I use
MacMakeup), using the program to "generate random" MAC address, "change" MAC address, wait a sec, then cycle the modem by unplugging it and replugging it. There you go.