Is the externally enclosed hard disk drive, formatted for use with Mac OS X?
Not sure about the Time Capule unit...
•Backing up with AirPort Time Capsule for the first time:
How about that Time Machine...?
•Mac Basics: Time Machine backs up your Mac
How do you have Time Machine software set?
•Apple - Support - Time Machine:
Have you tried making copies or clones of your system in
an external HDD without time machine or time capsule?
You could use CarbonCopyCloner, if your external is big.
What computer do you have, that needs a battery replaced?
Some portables with a 'pram' type battery, and desktops.
And some certainly do not encourage user take-apart.
Could be a few backup ideas in links.
Good luck & happy computing!