These error codes C1010007 and 800704C7 mainly occur when you are busy updating your mobile phone with Zune software. Depending on how full your phone is during the backup process these errors might show in the middle of the backup process. There are a few common fixes to these.
Your first problem could be the USB cable or port on your computer when it stops. Check your USB cable and also the port. Try and change the USB ports and plug the cable into another port such as the rear port on the computer. Dont use USB cable extensions as these tend to create problems where there is not enough electricity getting tot he phone. There can also be a USB error such as the tongue in the USB port being bent which is very common. You need to bend it upwards as the cable after a few months tends to bend the tongue down giving an error.
If this does not work then try another computer and see if it will work on the new computer. Try a different cable if possible. If this fails then you will need to take your phone into the mobile phone store for a check.
Note that even when you phone is disconnected the software on the phone will still be running. Dont run off the phone or remove it battery. Let it complete as it will normally reboot itself when done and the Zune software will try and connect again as the update would not have been done and your phone will be as what it was before you started the process.
If Zune does not recognise your phone then you can try the Microsoft Fix option.