I am getting this message: Time Machine could not complete backup. The backup disk image "/Volumes/D's Time Capsule/D's MacBook.sparsebundle" is already in use.
Switch off in Time Machine. Then remove the TC from Time Machine and from your network. Erase TC with the Airport Confirugarion Utility program. Select "rewrite with zero's". Multi erasing (7x or 35x) only prevent abuse of your back-up data by others. Then reinstall the TC back again to your network and switch on Time Machine and install the erased TC in Time Machine. It should work. Beware, your back-up files will be lost.
The problem is very likely a corrupt "xxx.inProgress"-file.