I use a program for my data recovery called Spinrite, which uses statistical analysis on 'bad' sectors of the hard drive to recover them. It will read a bit location of the hard drive hundreds of times and calculate the likeliest original value of the sector. It truly is phenomenal at recovery, and it leads me to believe the above is still true.
This isn't my program, but I've used this on multiple systems (including ones at work) to recover data. It's called Spinrite. It costs money, but it's worth every single penny (& it's not thousands of dollars which is usually what any of the drive recoveries we send for work cost). You can find it here: http://www.grc.com/spinrite.htm
I highly recommend SpinRite, if the drive is still detected by the bios spinrite will see it, fix it, move your data to a safe place on the drive and mark off the bad sections so data won't ever be written there again. Once it's done copy all the data off the drive and toss it.
Backup everything important ASAP to CD's or flash memory, or whatever; and order a replacement, then RMA the failing drive. Also, get a copy of spinrite through what ever means you want, burn the bootable CD, and shut down your machine. When you get the 1TB backup HDD, put it in your computer and boot from spinrite. Use spinrite to move all the data off the failing drive to the new one. Hopefully your drive will have survived being turned off and live to transfer the data.
You may have better luck in r/techsupport, but given that you asked here...
1/2: Odds are that the hard drive has some errors. I would advise backing the drive up as soon as possible, in the event that this is a sign of a larger failure approaching. I would do this before attempting any recovery. Once it's backed up, I'd look into using SpinRite to do a low-level sector analysis/recovery on the drive. This may or may not allow you to access the file (and missing folder), but I've had decent luck with it.
http://www.grc.com/spinrite.htm
You could try spinrite. It will take damn near forever, but its the best recovery app I've seen so far.
It really depends what you're having trouble with and why its not mounting, but its a good place to start. Remove the drive from the enclosure, and plug it in then boot spinrite and walk away for a few (hours). I've seen this program take upwards of days too so be patient. Then if it still doesnt work go pro.
For side work I usually charge $80 per hour with a $40 minimum, rounded to the nearest quarter hour.
For friends, I expect a 6 pack of Firemans 4 and depending on the work, a meal or gift card to Chick-Fil-A.
In your case, I would try to move the drive into another computer. If that worked, $40 plus the potential cost of an external drive that can hold all their data. If moving the drive doesn't work then I would try SpinRite and if that worked it would be $80 plus I would expect them to buy a copy of SpinRite.
Very, very tricky thing to do sometimes. Hard drives have an annoying habit of failing inconsistently. I've seen countless hard drives that behaved fine 90% of the time, and then would glitch. The best way to pinpoint the hard drive as the culprit is swap in a know-good one and let it run for a while.
If that's not an option, then there are any number of utilities that can sometimes help. SpinRite is one. SyrioForel mentioned a few others.
Suggestions:
Try using a Ubuntu live cd/usb and see if Ubuntu can see the hard drive. Have a new drive in the pc and set up the broken on as an external drive. If Ubuntu can see the broken hard drive and does let you copy data off of it it will be only for a short period of time. If this doesn't work try sprinrite http://www.grc.com/spinrite.htm
Also maybe try Spinrite to see if there are errors with the drive, and to fix them.
I hope you haven't thrown the drive out yet. I've seen lots of suggestions for backup solutions, but that doesn't help you here and now.
The only solution for belly-up drives is Spinrite, and I expect your time and effort compiling that TB is worth the $90 price tag. Plus, he gives refunds if it doesn't recover your data!
Hiren's Boot CD is my go-to fix everything disk. I believe it may have a copy of SpinRite on it. It has saved me on several occasions.
Sounds like a failing hard drive. Or, it became unseated. Lots of things can actually cause this. Bad RAm would stop the OS from reading the file system correctly for example.
http://support.microsoft.com/kb/555302
Irt means the computer can't read the file system well enough to boot. Try a program like Spin-Rite. http://www.grc.com/spinrite.htm
May try spinrite. If your files were corrupted it may be able to fix this issue.
You'll create a bootable SpinRite CD/DVD on another computer and then try and fix this one.