Great, got IP kicked from Roblox.?

One of my family members went to spam a forum and now my IP's on Roblox's blacklist. I sent them an e-mail to ask they lift it and ban my family member's account, but guess what, they said they "couldn't do anything about it", which I'm pretty sure is a lie. I'm not going to use a proxy because they are all God awful and I'm not going to risk getting malware in my computer. My last resort, but probably my only hope, is to reset my IP address. How should I do it? By the way, I want something more thorough than "open the properties of network 1 and poof it's changed." I'm considering hitting the reset on on my Linksys and deleting all of the cookies in my browser, but I'm afraid the Internet provider (Comcast) will be too dumb to recognize the address.