Time Machine essentially stops Mac responding

Question

I've recently posted on a problem I've had with a misbehaving time capsule.  Different problem now.
I have a fairly old Macbook Pro (one of the early monobody machines), 2.8G Core 2 Duo running 10.8.3. Until recently it's functioned well.  I turned Time Machine off a couple of weeks ago, and turned it back on earlier this week.
I've lost my old Time Machine backups, but am now trying to back up to a new, healthy Time Capsule.  Another mac I have has Time Machine working perfectly well on this Time Capsule.
Earlier I started a new backup and left the machine.  4 hours later I returned to find 50+ GB out of 200GB backed up, but the mac itself is pretty much non responsive.  It takes up to 20 seconds to switch between applications, then the spinning spectrum wheel is in evidence much of the time.
Some info on what I've done to try to diagnose the problem
I've verified the disk on the macbook, it verifies fine.  I've restarted in safe mode to clean up (whatever safe mode cleans up) then rebooted again.
I've tried switching to a different admin account which gives the same result.
Running Activity Monitor is interesting but not too informative (to me)  In short, nothing seems to be happening.  Not much CPU activity, ditto network or disk activity.  So nothing seems to be hogging the CPU.
The problem seems to be independent of whether I run over wireless or hard connect to the Time Capsule
If I stop the backup and turn Time Machine off the mac responds as normal.
If I turn Time Machine back on and it's waiting for the next scheduled backup, again, the mac responds as normal.  So it'd appear to be solely a problem when the TM backup process is actually "active"

Answer 1

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.
Enter the word "Starting" (without the quotes) in the String Matching text field. You should now see log messages with the words "Starting * backup," where * represents any of the words "automatic," "manual," or "standard." Note the timestamp of the last such message. Clear the text field and scroll back in the log to that time. 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 (command-C) to the Clipboard. Paste (command-V) into a reply to this message.
If there are runs of repeated messages, post only one example of each. Don't post many repetitions of the same message.
When posting a log extract, be selective. Don't post more than is requested.
Please do not indiscriminately dump thousands of lines from the log into this discussion.
Some personal information, such as the names of your files, may be included — anonymize before posting.