Time Machine Restore Slows Computer

Question

I have a 24" iMac (Early 2008) 3.06GHz Intel Core 2 Duo computer. The original hard drive failed last week and I had it replaced with a new 1TB HD at a local Apple Premium Service Provider shop.  The computer worked like new when I got it back...and then I restored my backup from Time Machine. 
So I've had this Mac since 2008 and since then I have gone through almost all the OS X updates.  I have downloaded and installed tons of apps, which over the years have become out-of-date and thus no longer work with the current OS.  I have downloaded countless of albums and movies, tv shows etc, etc.  I have deleted some of this information over the years.  I have also been through a few different external hd's using Time Machine, but I always transferred all the old information to the new ones.  Could someone tell me if bits of leftover information are now saved on my HD and are thus causing the computer to perform extremely slow?  If this is the case, what would be the best approach to deleting this information?  Thanks in advance!

Answer 1

When you have the problem, note the exact time: hour, minute, second.
If you have more than one user account, these instructions must be carried out as an 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. Click Utilities, then Console in the icon grid.
Make sure the title of the Console window is All Messages. If it isn't, select All Messages from the SYSTEM LOG QUERIES menu on the left. If you don't see that menu, select
View ▹ Show Log List
from the menu bar.
Each message in the log begins with the date and time when it was entered. Scroll back to the time you noted above. Select the messages entered from then until the end of the episode, or until they start to repeat, whichever comes first. Copy the messages to the Clipboard by pressing the key combination command-C. Paste into a reply to this message (command-V).
The log contains a vast amount of information, almost all of it useless for solving any particular problem. When posting a log extract, be selective. In most cases, a few dozen lines are more than enough. It is never necessary or helpful to post more than about 100 lines. "The more, the better" is not the rule here.
Please do not indiscriminately dump thousands of lines from the log into this discussion.
Important: Some private information, such as your name, may appear in the log. Anonymize before posting.