I recently upgraded to OS X 10.9.2 Mavericks.
Did you upgrade from earlier version of Mavericks or an earlier OS.. You can always revert you know.. like if you were on mountain lion.. reboot the computer to the boot options and select the backup and go back.. it is well worth thinking about.
If you are have simply upgraded from earlier Mavericks.. then I guess you just need to live with it.
I shouldn't think the MyBook Live would fail with just an update.
I have no idea how to help you with the WD drive.. you would need to contact WD about if they have updated firmware or some such to make it compatible.
But I should be able to help you with the TC.
What model is it exactly.. A1xxx from the base. eg A1254 is gen1 A1302 is gen2 A1355 is gen3. All of those have 1TB disks.
Reset it to factory.. and plug it into the computer by ethernet.
Universal Factory Reset.. any model TC or AE.
Unplug your TC/AE from power or turn off at the power point.
Hold in reset. and power the TC/AE back on.. all without releasing reset and keep holding in for about 10sec. (this is often difficult without a 2nd person or a 3rd arm).
Release it when the status light flashes rapidly. If it doesn’t flash rapidly you have missed it and try again.
Note..
Be Gentle! Feel the switch click on. It has a positive feel.. add no more pressure after that.
TC/AE will reboot after a couple of minutes with default factory settings and will wipe out previous configurations of the router.
No files are deleted on the hard disk in a TC.. No reset of the TC deletes files.. to do that you use erase from the airport utility.
In the computer make sure you have IPv6 set to link-local for ethernet (and wireless for later connection).
Does the TC show as device that can be configured in the utility?
If not do you have an older computer running either windows or any os up to ML.. or even iOS device and you can download the iOS version airport utility which works a lot better than the Mavericks one.
Is the led on the TC flashing amber? Does the ethernet LED turn on to show connectivity on the TC?
Tell us more info if it fails.