Single User Mode Fails on Macbook Air - still waiting for root

Hi, we've had intermittent issues with this machine - I recently cleaned it up/refreshed it and gave it to my son and his GF for use in Spain. So, I'm missing some details but will try to recall re the machine. They can't boot the machine - they get the grey logo with the slash, which had happened previously. I believe that a series of PRAM/SCM resets and perhaps a startup via Internet Recovery sorted it out in the past. Steps taken so far:

- I've had him try safe mode, recovery mode, PRAM reset, SCM reset - all to no avail

- Next, we tried booting and going into the Apple Hardware Test (AHT) mode/diagnostics. ATH did initialize, the test started, but it froze about 70% of the way through and we tried it a 2nd time but the same result occurred. Only attempted the Basic test.

- Lastly, we tried to boot in Single User Mode, because I wanted him to get to the command line so we could run fsck, etc. During Single User Mode boot/initialization, a failure occurred - a couple of lines are:

CoreStorageFsck: LVG on disk0s2 is corrupt (800000008: incorrect block type)

.

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Still waiting for root device

I'm suspecting a HD failure, but have seen some hints on forums that PRAM battery or other issues sometimes are related. I don't have the machine with me and forgot to get the spec details (it's middle of the night there now) but can add to the thread tomorrow. I've grabbed the model/specs that I believe are accurate - see below. Will update if necessary..

Also, I've attached a screenshot of the dump/fail in Single User Mode

Thanks for any input/advice.

MacBook (13-inch, Late 2009)

• 2.26GHz Intel Core 2 Duo processor with 3MB on-chip shared L2 cache running 1:1 with processor speed
• 1066MHz frontside bus
• 4GB SDRAM
• 320GB 5400-rpm Serial ATA hard disk drive