Your usable IP information is going to be in the LAN block. Most service providers should take the first usable IP from that block to assign to their equipment. This also is what you end up configuring as your devices default gateway.
In the case of 63.145.XX.XX, let's assume this block starts at 0.
63.145.xx.0 - network address
63.145.xx.1 - Century Link router port AKA your device's default gateway.
63.145.xx.2-6 - All assignable IPs for your equipment. Pick one to statically assign to your new router.
63.145.xx.7 - broadcast address
So for example, you could use 63.145.xx.2, with a mask of 255.255.255.248, and a gateway of 63.145.xx.1 for your static IP configuration.
Obviously this changes depending on the exact assignment of your IP block but hopefully this paints a clear enough picture of how you should assign your static IP.
Thanks for the reply. I really appreciate your help. Everything is working again.