Q: What is wrong with my Mac Pro?

Apple Hardware test will not always identify problems. You may want to run it more than once, to see if detects problems. Between the disk hardware and the filesystem, there are layers of software.

You can try Mac OS X: Hvad er Sikker start, Sikker tilstand?

The Apple Hardware Test does NOT test the internal HDD so it will be of no value determining if the HDD is faulty or not.  If you tried Disk Utility from the 4 option menu provided by the recovery HDD and it came back indicating it cannot be repaired, back up as much data as you can and replace it.

Ciao.

If you cannot get into the HDD now, replace it and install it into an enclosure.  When the MBP is functional with the new HDD, attach the old one to the MBP via USB.  Download data recovery software from the Internet and see if that will work.  Most developers have a trial version that will indicate whether you will be successful or not.  That way you do not spend money on a lost cause.

The last alternative is to engage a professional data recovery firm.  It will be very expensive and will come with NO guarantees of success.

Ciao.

You have two issues.

1. The Repair fails due to disk space issues.

2. If you can boot from an external media, you can delete files form Downloads, etc.and clean up so the fsck can succeed.

3. You can also try Target Disk mode, if you have another Mac, and access this disk drive and extract files.

On the website, search for Target Disk Mode under support. You should see an article about it.

OS X Mavericks: Overfør arkiver mellem to computere ved at bruge den ene som ekstern harddisk

Yes, it should work, even if the internal drive is unbootable, Target Disk Mode allows another Mac to read the internal disk.

Booting from external USB should allow you to treat the internal drive has a regular disk and clean up files.