Can't backup in time machine or upgrade to Maverick or Yosemite, can I still transfer via thunderbolt?

Question

I have a macbook pro 17 inch, Mid 2010 OSX 10.8.5. I currently have no back up as both my previous seagate and now my Lacie external drives won't back it up with the time machine. I get a box stating an error occurred and it quits after about 10GBs. In addition, the laptop fails to install Maverick and Yosemite when I have attempted to install them. For work I have just got a 15 inch Macbook Pro Retina. I obviously need all the data and files from my old laptop, if I were to transfer all the programs etc, would it likely transfer the problem that stops my computer from backing up? or is it more likely a hard drive problem and won't affect the new laptop? 
I have followed trouble shoot and looked at previous posts but haven't been able to find a solution. Also I have gone on disk utility and verified the disk and all is fine there, so I am unsure what the problem is.
Ideally I can get working on the new 15" soon but I don't want to transfer over any problems.
Thanks

Answer 1

These instructions must be carried out as an administrator. If you have only one user account, you are the administrator.
Launch the Console application in any of the following ways:
☞ Enter the first few letters of its name into a Spotlight search. Select it in the results (it should be at the top.)
☞ In the Finder, select Go ▹ Utilities from the menu bar, or press the key combination shift-command-U. The application is in the folder that opens.
☞ Open LaunchPad and start typing the name.
The title of the Console window should be All Messages. If it isn't, select
          SYSTEM LOG QUERIES ▹ All Messages
from the log list on the left. If you don't see that list, select
          View ▹ Show Log List
from the menu bar at the top of the screen.
In the top right corner of the Console window, there's a search box labeled Filter. Initially the words "String Matching" are shown in that box. Enter the word "Starting" (without the quotes.) You should now see log messages with the words "Starting * backup," where * represents any of the words "automatic," "manual," or "standard."
Each message in the log begins with the date and time when it was entered. Note the timestamp of the last "Starting" message that corresponds to the beginning of an an abnormal backup. Now
CLEAR THE WORD "Starting" FROM THE TEXT FIELD
so that all messages are showing, and scroll back in the log to the time you noted. Select the messages timestamped from then until the end of the backup, or the end of the log if that's not clear. Copy them to the Clipboard by pressing the key combination command-C. Paste into a reply to this message by pressing command-V.
☞ If all you see are messages that contain the word "Starting," you didn't clear the text field.
☞ The log contains a vast amount of information, almost all of which is irrelevant to solving any particular problem. When posting a log extract, be selective. Don't post more than is requested.
Please don't indiscriminately dump thousands of lines from the log into this discussion.
Please don't post screenshots of log messages—post the text.
☞ Some private information, such as your name, may appear in the log. Anonymize before posting.