I don't know diddly squat about TimeMachine specifics, but saw your post drifting off so I thought I'd better answer.
Pondini is our resident TM expert, his web page is here
I do advise this, TM is sort of a trap, you can't access the files directly too easily, without using additional expensive software. Only another Mac and only if TM works, and only to another like OS X verison.
So if you have ANY opportunity to copy your user files to a normal regular storage drive and disconnect it you should take it before erasing your copy on the internal drive.
You will likely find a huge amount of information here on my old thread if your attempting data recovery yourself from the main internal drive that is failing to boot, it's more geeky and involved
once your personal data is safe in a neutral format, if the TM restore doesn't work you can always fall back on a manual reinstall of everything and returning your files.
If you have to do a bit level recovery of TM, then that's going to cost $99 for DataRescue and blank hard drive to send the data too. It's occured before here so I'm just watching out for you.
Also later consider using Carbon Copy Cloner, it clones, it option key boots, and the files (not filevulted) are accessible by any Mac, Linux or WinPC (with MacDrive installed), unlike TM.
My main boot drive started acting like it's in slow motion 2 days ago. No matter what I do (DiskWarrior, Disk Utility, zap PRAM, fix permissions) nothing seems to help. Every mouse click or movement gives me the dreaded spinnin wheel and it hangs for about 5 min and then does what it's supposed to do. I have logged into a new account w/ no special 3rd party apps or utilities and it still does the same thing. Hard drive diagnostics say my hard drive is ok. I have tried reinstalling the 10.6.8 combo update but that hangs after a few minutes of starting. I am stymied.
Could be a failing drive, could be Lion when you boot doing something
Disconnect all other drives etc., except the 10.6.8 boot drive, lets flush everything.
hold Shift upon booting, this is Safe mode and fixes things, reboot
then SMC reset, PRAM reset
Run all of OnyX checks, maintainance and cleaning then reboot at the end
If you have AppleJack already installed hold command S at startup of 10.6.8 and Applejack AUTO and press enter.
This mega cocktail will do plenty to rebuild everything and may catch your issue.
If your still having problems I would try to isolate it, if it occurs only if your connected to the Internet, or after the machine has booted Lion etc.
Narrow it down. It might be failing sectors on the drive, this has been known to cause beachballs as the hardware is trying to read from failing sectors, once it gets the information it should be transfering it to a new better sector and mapping off the bad one.
You can expidite this process when you fresh install, by erasing the entire drive (or Free space only) with Zero function in Disk Utility before laying large amounts of data on the drive. (like a OS or partition)
I was able to restore my drive from Time Machine and it was successful but some of the Apple apps quit unexpectedly ... Mail, Safari, iTunes. I tried everything you suggested and ran reset SMC, PRAM, Onyx and still no luck.
This is what I get when Mail quits:
Process: Mail 
Version: 4.5 (1084)
Build Info: Mail-10840000~1
Code Type: X86-64 (Native)
Parent Process: launchd 
Date/Time: 2012-02-28 22:28:23.717 -0500
OS Version: Mac OS X 10.6.8 (10K549)
Report Version: 6
Interval Since Last Report: 3452800 sec
Crashes Since Last Report: 13
Per-App Interval Since Last Report: 2089353 sec
Per-App Crashes Since Last Report: 3
Anonymous UUID: 8482E2D5-CBAA-4E14-B584-049644684330
Exception Type: EXC_BAD_ACCESS (SIGSEGV)
Exception Codes: KERN_INVALID_ADDRESS at 0x00000000ffffffff
Crashed Thread: 0 Dispatch queue: com.apple.main-thread
Application Specific Information:
There's a lot more but it was quite long.
Any idea what may be going on?
I fixed it! I restored my Time Machine to an earlier backup ... a January date rather than a week ago, and everything ran perfectly, exxcept for Safari ... it would quit as before. Then the auto Apple Update notice popped up and I saw a Safari update so ran it and now everything is working again as it was.
Thanks for your help.