Mavericks is a pain..
I strongly recommend you.
1. Full reset.
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.
2. When you redo the setup, give the TC all short names with no spaces and pure alphanumeric.
Your current name is a problem. It is over long.. has spaces and apostrophe. This is what apple suggests in the wizard.. but Mavericks has changed over to SMB as default network protocol. This messes things up something chronic.
3. You will need to reset the TM to locate the old backups on the renamed TC. You will need to do it on the other computer that is using the TC as well.
See A4 here. http://pondini.org/TM/Troubleshooting.html
4. If you continue to have issues.. manually mount the hard disk.
In finder, use Go/Connect to server.
Type in AFP://TCname.local (where you replace the TCname with your new short name.. and you need to add the domain which is by default local. )
OR
You can use the IP address if it is static.. ie the TC is in router mode.
AFP://10.0.1.1 (which is the default IP.. replace with actual IP).
When the computer locates the resource it will ask for a password.. type that in .. public by default.. or whatever you changed the disk access to.
