Old saying.......
Make just one change on a network......and just about everything else on the network will change.
Your tagline......MacBook Pro, Mac OS X (10.6.1).......indicates that you might have originally set up the Time Capsule to "join" your network using wireless and operate as a back up hard drive in that manner. Would that be correct?
If yes, AirPort Utility in Yosemite, Mavericks, Mountain Lion, and Lion no longer offers the option for the Time Capsule to connect and "join" using wireless......except....in the case where it connects to another Apple router.
Unless your new router is an Apple device, the Time Capsule will need to be permanently connected to your new router using a wired Ethernet cable connection....unless you consider the option below of using an older Mac or PC to try to set up the Time Capsule.
Reset the Time Capsule back to factory default settings
Connect an Ethernet cable from one of the LAN <--> ports on the new router to the WAN "O" port on the Time Capsule
Use AirPort Utility to configure the Time Capsule to create a network
Once the setup is complete, you can go back in using AirPort Utility and turn off the wireless function of the Time Capsule if you do not need another wireless network.
If you cannot consider the Ethernet connection method, and instead you want to configure the Time Capsule to connect using wireless only, that might still be possible, but you will need a Mac running the Leopard (10.5.x) or Snow Leopard (10.6.x) operating systems, or a PC with AirPort Utility installed on the device to be able to try to set up the Time Capsule this way.
No guarantees that this will work, as your new router may not be compatible, wireless wise, with the Time Capsule. Much has changed in the last 3-4 years.
This will be one of those times where you will not know if something will work on your network until you try it out on your network.