As stated in the previous posts, changing your internal IP address has little to no relevance to "hacking" or preventing getting caught from whatever the malicious activity may be. As a client of your ISP you HAVE THE RIGHT to have your external IP changed whenever you wish. Due to lease times and other measures, just unplugging or resetting your router and or modem probably will not change your external IP address.
If you really wish to change your IP address then all you have to do is call your ISP and ask them to release and renew your account with a new IP address. The longest time it will take you is probably going to be spent listening to hold music. But just changing your external IP address with your ISP is not saving you from getting caught from doing anything over the net. Your ISP always has a record of what IP you had/have and when you have/had it.