My time machine will not mount under 'devices'

Question

I restored my mac air because of system corruptions.  I went to migrate my former build's user profile to the new system, but when I entered time machine it only showed me backups from the rebuilt system.  The only way I restored my files/settings was by navigating to my old backups in the finder (under devices in the finder) and copy/paste/replace into the new user profile.
Now I have 2 problems despite having searched the apple support docs and the forum. 
First, I want to manage my old user time machine backups through my time machine app.  All I am able to access are the 4 backups made in the new system since the reinstallation.  That gives me a gap of several months back to when I purchased my air.  How can I access them while in my current user profile?
Second, my time capsule isn't mounting under devices.  I've got "show external discs" selected in finder prefs.  Obviously, it was showing earlier because that's how I got my files reloaded.
Which of course has me in a catch 22.  Even if I knew how to access my missing backups via time machine, I can't access the time capsule to set it up in the first place.....
Advice?

Answer 1

First, I want to manage my old user time machine backups through my time machine app.
Manage meaning what.. an old backup cannot really be managed.. it is a backup.. you restore from it.. you don't manage it.
But if you merely mean to open it.. and TM is refusing to allow it to be opened.. well that is part and parcel of the Mavericks TM... !!
Pondini has instructions for opening TM backups from other Macs.. same rules apply here.
See Q14-17 here. 16 and 17 being the key ones.
http://pondini.org/TM/FAQ.html
Once you are out of a TM backup you cannot then use it for continuing backups.. You can try and inherit it but I think you are too late.. that should have been attempted immediately.
See B5 and B6 here.
http://pondini.org/TM/Troubleshooting.html
Second, my time capsule isn't mounting under devices.
This is typical Mavericks excellent networking.
Time Capsule should appear under shared not devices.. Once you mount the backup it will appear under devices but not until mounted.
1. I strongly recommend full factory reset of the Time Capsule.
No files on the disk will be lost.
The Factory Reset universal
Unplug your TC/AE. Hold in reset. and power the TC/AE back on..  all without releasing reset and keep holding in for about 10sec. The time is not important.. it is the front LED rapid flashing that indicates you are in factory mode.
Release reset.
If it doesn’t flash rapidly you have released reset at some point and try again.
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.
No files are deleted on the hard disk.. No reset of the TC deletes files.. to do that you use erase from the airport utility.
2. Redo the setup with all short names, no spaces and pure alphanumeric.
See apple documents which finally have fessed up to some of this.
OS X Mavericks: Time Machine problems
Although apple says 27 characters max.. please keep it under 10 if you can and 20max. eg TCgenx as base station name.. replace x with actual gen.
TCwifi for wireless name. Do not accept the names the airport utility will give you.
3. Mount the TC manually in Finder. Use Go, Connect to Server.
AFP://TCgenx.local (where you replace with your actual network name.. same as the name if you have followed the rules.. local is TC domain and helps).
When asked for disk password supply that and remember to save it in the keychain.
4. Reset TM see A4 in Pondini troubleshooting.
5. You will need to point TM to the newly named TC.. it will take some time for it to pickup the current TM backup but that should not be a problem once it starts backup.
One thing you should do before starting.. change ipv6 setting on the computer to link-local only.