My router was damaged and has been replaced, as such I am using a new name & password for the wifi connection at home. However, somehow I am lost in getting my time machine "hook" to the wifi.
It appears that the wireless settings on your new router and the Time Capsule are not compatible. The Time Capsule wants to see a wireless security setting of WPA2 Personal on your new router.
That means that the setting on the new wireless router for wireless security must be set to use that same WPA2 Personal setting. Otherwise, the new router and Time Capsule will not be able to establish a connection using wireless only.
If you have tried the set up multiple times and the TC will not connect using wireless only.....you will need to connect the Time Capsule to your new router using a permanent wired Ethernet connection.