The old Time Capsule needs to be accessed in total isolation. That would mean that you need to temporarily power off any other AirPort Time Capsules or other Apple router(s) that you have, so you may want to try this late at night or another time when folks won't complain that the Internet is down.
Connect an Ethernet cable from the Mac Mini to one of the three LAN <--> ports on the Time Capsule.
Open up AirPort Utility on your Mac Mini
Click the File menu in the upper left hand corner of the screen and select Configure Other.
For Address, Enter
10.0.1.1
Leave the Password area blank for now
Click OK
If things work......you will see a summary page of settings with tabs for Summary, Base Station, Internet, Wireless, Network, Disks
if you are asked for a password above.....Enter
public
If you cannot access the settings with the steps above, then I know of no other way to get into the old Time Capsule.
Please report on your results so far, and we'll continue with the procedure to erase the disk and review some options if the Summary page appears.