I can't access my files on my old Time Machine back up on my newer iMac

Question

Okay, so I’m in a bit of a mess here.
I did have an old Macbook running on Snow Leopard 10.6.8 which died on me.
Luckily I managed to get a few Time Machine Back Ups  before I passed away . These back ups are
saved on a non-Apple external HD.
I recently inherited an iMac ( from 2009) which was also
running on Snow Leopard 10.6.8. I got very excited and hastily up graded the OS
to Yosemite.
This iMac belonged to a friend, and I did not have the Snow
Leopard disc to perform a factory restore so I decided to simple delete their
account (System Admin account) from the iMac and keep the account they made for
me with the intentions of making that the main account.
After upgrading to Yosemite and deleting the System Admin account and making
myself the main account holder on the iMac I tried to access my files on my
external HD to manually move them onto the new iMac ( such as my photos,
videos, music, logic files, documents etc).
This is where I encountered my problem. I can no longer
access my folders on my external HD. It tells me I do not have permission to do
so, with a little red stop sign on front of all of these folders and files.
Is there any way I can fix this without having to buy a Snow Leopard disc? AND
IF I do perform a factory restore will my files in my HD still be locked?
Thank you in advance.

Answer 1

I managed to get a few Time Machine Back Ups  before I passed away
I'm not sure whether a ghost can do this, but if you were still alive, you could do as follows.
First make sure you have read & write access to the folder you're trying to restore to. You should be able to see its contents in the Finder, and to move files in and out of it.
This is an exception to the rule that you should never make any changes to backup data. I've tested this procedure in OS X 10.8 only. It should work with later versions, but I don't know whether it works in earlier versions. Use it only for files that were backed up from your home folder, or a folder on another volume created by you, and would normally be writable by you. Do not touch backups of system or application files.
In the Finder (not in the time-travel view), navigate to the backup volume, then to the folder named "Backups.backupdb", and then to the snapshot you want to restore from. The snapshots are folders labeled with the date when they were created. Inside each of those folders is a file hierarchy like the one on the volume that was backed up. Descend through the hierarchy until you come to a folder named "Users," and inside that, a folder with your user name. The procedure will be different if you're trying to restore files on another volume.
Select the folder and open the Info dialog (command-I). Click the padlock icon in the lower right corner of the window and authenticate. In the Sharing & Permissions section, give your account Read & Write access. You may have to close the dialog and repeat this step in order for the change to show up. Then click the gear icon and select
          Apply to Enclosed Items
from the popup menu.
Try the restore operation again, in the time-travel interface.