So you're trying to connect/backup to your Time Capsule (1st Gen OS7.6.1) and it seems like it just died...? But you can still connect using the AirPort Utility? And it still pings.... Oh but wait you can connect to the disc using...... Yes Windows file sharing protocol (SMB/Samba). What's going on?!
It seems that Apple's File Sharing (AFP) server just dies - quite often. Indeed it would seem that the Time Capsule's AFP implementation is flakier than their Windows (SMB) server. That's handy for an Apple product?!
The annoying thing is that whilst you can connect to the thing using the AirPort Utility you can't restart it - it just hangs. So you have go and turn it on and off.