Task Sequence: <Task_Sequence_Name> has failed with the error code (0x80070070). For more information, please contact your system administrator or helpdesk operator.
I have received the above error just before copying/staging the boot media, when I have tried to deploy Windows 7 image using deploy task sequence. I am sure I have enough space on the local drive but seems to be an issue copying the WinPE image to C drive.
To resolve the issue, hit F8 to open the command prompt in winPE. Then run DiskPart, then List Disk, then Select disk 0, then clean
Restart the target machine and try again. This time it should work without task sequence error 0x80070070.