Post-backup Issues

Hello.
After dealing for a couple of days with the incompetence and stupidity of the pseudo technicians at the local Apple authorised store i decide to ask here where i know there is people that, unlike those idiots know how to use a mac.

Long story short, i take my mac to a little repair, ram upgrade and... why not update the OsX on the go... somehow in the middle of this they erase the hard disk after making a parcial and very stupid backup of what they believe have to be backed up and whats not... anyway, leaving aside the around 30Gb of personal data lost and the stupid story of how they try to recover it (somehow the recovering tools only save porn from the browsers' cache that i didn't even knew can be recovered but nothing remotely useful LOL)
...Anyway, they leave the carcass of the old user on the desktop and left me to figure it out what to do with it, after a couple of "go to folder" commands i found out that the old library with all the application support and stuff was still there but invisible... there is no "show library" 'cuz its not a user folder anymore but i was happy it was there, but somehow nothing inside can be moved without make a copy, changing permissions didn't change anything and holding command while dragging the files doesn't work neither, is there anyway to un-bless the old library folder?

If anyone can help me please because i fell im getting down and down on a spiral staircase to hell

 

Well, the thing was like this, i have a mac mini 2011 that was running on Lion since new, i couldn't move to mavericks back then because i was using software that will not work and other stuff... after a issues on the hardware i take it to the tech to fix it, once it was there they offer to upgrade the OS, i didn't do it myself because i know that if i install "el capitan" on it, it will probably become slow as hell... and apple denies to let you download any Os version that is not the latest... even so the tech told me that they can install mavericks with no issue (not really sure how)
Once we were there, they told me that they will back up the HD and make the OS upgrade (I have mostly of the data backed up manually on external HDDs but not a time machine restore or anything like that... not sure why) anyway, i assume that they will make the backup (with time machine) in case of anything going wrong with the install, but no, they manually backed up what they wanted and then make a clean install erasing the hard disk (they insist that its the policy... i think thats retarded)
Anyway they left the old hard disk leftovers in a folder called backup on the desktop like if we still were in 1998...

The MacOs is working fine, restoring the system won't help, im trying to get the files out of the phantom library folder on the old user carcass inside the backup folder.
thanks.