Back-up with Time Capsule using Ethernet?

Question

I want to backup 1TB of data from an iMac HD using the iMac's ethernet connection. This is not a first connection to the Time Capsule ; I need to recreate the backup after a hard disk failure and replacement.
Time Capsule sticks to the wireless network, and after 7 days running estimates another 7 days to complete the backup.  Attempts to stop and restart, or change configuration result in a complete restart of the backup.
The TC is connected to iMac ethernet port and on router wireless network, on a wireless "N" connection.
Hardware/Software:
iMac 2010 model running OS10.8.3 Mountain Lion
Time Capsule 4th Generation
Airport Utiility 6.2
Solutions tried after researching various support sites:
Turned off wireless network on iMac - disc drops from network and cannot be mounted using ethernet alone
In Network Preferences rearranged service order to give ethernet priority
Removed TC from wireless network (through Airport Utility); disc cannot mount without a wireless connection, so reinstalled it as a wireless device again
Erased TCs hard disk (using airport utility) to restart backup
Removed TC from Time Machine preferences, and reinstalled adding TC as a new disk
Turned off anti-virus programme (Clam Anti-Virus)
None of this has worked.  Are there ideas that would speed this process using ethernet?

Answer 1

Thank you for your help, and the very useful link to Time Machine support.
Unfortunately your solution didn't work.  I went through the process a couple of times to make sure that I had it right, but I still couldn't connect, mount or identify the TC, but it did lead me find a solution that worked:
TC factory reset
Locate the TC identifying data (in my case this was "Time Capsule b5c917"); Airport Utility locates the disc as part of the preliminary setup process
Did not go any further with setup, or reinstall the network connection (through Airport Utility); so flashing yellow light on TC
Connect ethernet cable
Shut down Airport Utility
Turn off wireless on iMac
Go to Finder, select Go drop down menu. Go to connection history on "Connect to Server" (Clock symbol on right of display) and click to display drop down of previous connections, select the TC name matching the identifying TC data to connect
TC is now connected through ethernet and starts back-up, recommencing where previously halted session ended, and estimated back-up completion reduces from 7 days to 12 hours
At completion dismount disc and disconnect ethernet
Open Airport Utility and setup TC as a wireless device (using the standard Apple process)
Open Time Machine and remove ethernet connected TC from backup disc list
Add newly setup TC as a wireless backup device in Time Machine
Test backup using wireless connection
Success. !
This is not an elegant or straightforward solution, but it worked, and solved a problem that has bugged me since getting the Time Capsule.  Thank you again for your help.
The same process should also work for an ethernet connection to restore data to a Mac.  I have previously used a wireless connection for a system restore, and it is painfully slow.
I hope this discussion helps others with the same frustrating problem, and wakes Apple up.  Apple need to do a much better job of explaining alternative methods of connecting Time Capsules, especially where large amounts of data are involved.  Expecting a wireless connection to run for 14 days to complete a backup (or restore) is just not practical, reasonable, or acceptable.