The Time Capsule will pick up the correct IP address automatically when it has been configured correctly to connect to your new provider's modem.
So, you must start all over again and reset the Time Capsule back to factory default settings, and then set it up again.
We can provide tips on how to do this if you need them, but we would need to know what operating system your Mac is using.......since (10.5.2) mentioned in your profile is 7-8 years old, and (10.4.11) is even older.
We would also need to know the make and model number of the "modem" that your provider has furnished to you as well.