A red light means the modem is rebooting. However, if it continues to be red for more than a couple minutes, it could indicate hardware failure.
If your modem is plugged into a surge protector or UPS system, unplug it and connect it directly to the wall outlet. Even if you're not using a surge protector, you can "power cycle" the modem by unplugging it, waiting 30 seconds and reconnecting. In a few moments, the modem should reboot and come back online.
If the light is still red, contact CenturyLink tech support for help.