Sounds like the Mavericks bugs may have crawled into your Mac and changed a few settings.
Open System Preferences (gear icon on the dock)
Click on WiFi on the left to highlight it, then click Advanced at the lower right
Click the TCP/IP tab
Make sure that the setting for iPv6 is set to Link Local
Click OK, then click Apply and close the windows
Thenn repeat the sequence above, except this time click Ethernet to highlight it and then click Advances
Be sure to click OK, then click Apply and close the windows
Restart the Time Capsule. Then, restart the Mac and see if the Time Capsule will appear.
Bob, I regularly do the Recovery trip, that is why I am so sure that my Mavericks is "clean" (I test a lot, that's why I have to be sure). The only thing that I permit myself is hibernatemode 0, and a locked sleepimage of zero bytes, but that has nothing to do with this "issue" (explanation below in annex).
I did the trick with the ethernet cable: now I see it, but "greyed out" I can not enter.
Funny, because in ML with 5.6 it was the same as in SL (worked perfectly, and in WiFi). 5.6 runs in ML, can not be installed, but no way to run it in Mavericks.
Well, now with your help, I have found my second "quirk" in Mavericks....
Annex: The first "quirk" is the hibernatemode=0 setting (in MBP): if you do that in earlier OS it will prevent the writing of a sleepimage (which was the same size as Ram); in Mavericks there still is a sleepimage even if you set hibernatemode=0, now the sleepimage however is about 1.1GB (only, but still to be avoided on a SSD). If you put a locked sleepimage of 0 bytes in the vm folder, a Swapfile of 1.1GB is written. This really is stinking.
Thanks for your help,
I think if you reset the TC it will appear. The problem seems to be when the TC is still configured.
Apple made a change which I think is key to understanding this.. in Mavericks, SMB is now the default network protocol.
It is almost mentioned in passing.
Macs running OS X 10.9 Mavericks will automatically default to using SMB2 when talking to each other, and fall back to AFP when file sharing with Macs running previous versions of OS X or when working with Time Machine backups.
Open network utilities in the Mac and run the netstat scan so you can find the TC.
Remember its name on a network is not what you named it, if the naming is wrong for SMB.
So Fred Blog's Airport Time Capsule is not valid.
Apple reinterpret it to Fred-Blogs-Airport-Time-Capsule.local (spaces and illegal characters removed).
Go into Finder and force the connection to AFP via Go, Connect to Server.
AFP://TCname.local (TCname is the network name which you find in netstat scan).
You will then be asked for the password which you enter.. public by default.
Then try again with the utility.
From now on.. stick with naming everything using SMB rules.. short, no spaces and pure alphanumeric. (actually it is not quite that strict but it is easier to follow it).