osx - Partition corruption, still can see files in single user mode, would like to retrieve files

The problem started after forcing the mac to shutdown. Since then, when trying to boot, it stays stuck at the grey apple with spinning wheel. I've tried a few generic things to be able to access my data on my internal drive without success. I first tried booting on the restore partition from mountain lion, but the same apple with spinning wheel issue happens, which makes me think that it's the partition that's corrupted and not the volume.

I've tried booting the iMac in Target mode and do the following:

1) I've tried using Disk Utility to repair the disk, but when trying to "Repair Disk" on the hardware item (not the volume one), the output gives:

Verifying and repairing partition map for “AAPL FireWire Target Media”
Checking prerequisites
Problems were encountered during repair of the partition map
Error: Some information was unavailable during an internal lookup

2) Data Rescue and Disk Warrior hang when I open them and when the Target disk is connected, but don't when I disconnect it.

What make me think that some data can be saved is the following

3) Using single user mode, I can navigate through the different users’ folders, I can even open their text files. Doing the fsck -fy command outputs: The Volume Macintosh HD appears to be OK.

Doing the /sbin/mount -uw / command, it outputs

SATA WARNING: Enable auto-activate failed
disk0s2: I/0 error.

followed by a few lines of gibberish followed by:

hfs: cat_delete() failed to delete thread record on volume Macintosh HD
hfs: Runtime corruption detected on Macintosh HD, fsck will be forced on     next mount
hfs_remove_orphans: failed to start transaction
hfs: hfc_btree_open: hfs_getnewvnode error 2

So I can’t mount the internal drive and I can’t seem to be able to mount an external drive to copy my files to it (since I can't create the destination folder for the device to mount to it). It seems that there’s no network connection in single user mode (unless I’m missing something), so I don’t believe I can send the data through networking and my laptop refuses to mount the Target disk.

There are some important documents I would like to save and I was wondering if there was some way to access the files on the hard drive the same way single user mode does it?

Thanks a lot for any answers!

Try to treat the drive as a simple block device and use dd to copy the sectors to the external hard drive. This would bypass any logical errors with the partitions and volumes. The fact that you got an I/O error might indicate a physical problem in a critical area of the internal drive. Then attempt recovery from that external copy, perhaps onto another drive if you have one.

It would be useful to know if dd fails at some point, especially early where critical structures might be. Unfortunately, getting output on it requires getting its process ID when it starts (e.g. by running it in the background) and then doing a

kill -SIGINFO process-ID

as needed. (That's SIGINFO and not USR1 which Linux uses.) To skip over trouble spots, include the option conv=noerror,sync. If the copy gets stuck, you can even try seeking on both the input and output to avoid those spots entirely, copying in chunks from the back to the front, etc.

Note that dd is quite dangerous, so it might be safer to use something like GNU ddrescue (never tried it myself).

Thanks for the answers, but I was able to simply mount an external drive into the /tmp folder. That way, I was able to copy all my files to it.