Restoring from Time Machine doesn't work

I am attempting to restore from Time Machine on my 13" Late 2008 MacBook, but the restore stops about halfway through.

Some background information: A few weeks ago my computer started exhibiting some weird behaviour. It would turn the disk off or log me out after a few hours (I typically sleep with it on and use at as my alarm clock). Then, apps would crash and quit unexpectedly. It would kick in the HDD when I was not using anything that required it, and the fan would turn on for no reason. Then the worst thing happened: Some days I would get the dreaded "You need to restart your computer" screen multiple times. It almost seems like a virus. The problems persist after multiple PRAM and SMC resets. Sure enough, I tried turning on my computer yesterday and it just won't even start. It would give me the Apple logo, a spinny loading indicator, and then it would give me a very slow progress bar. As soon as the progress bar gets to about one tenth of the way, the computer turns off.

I have everything backed up to a very recent Time Machine. I opened the computer in Recovery Mode and verified the disk. It needed repair. So I repaired it, and it said the repair was unsuccessful and needed to be restored. So I tried restoring it. I ended up having to erase Macintosh HD and reinstalling Lion (which thankfully I could do over the Internet). After reinstalling that, I tried "Restore from Time Machine." It got to about 30% of the restoration and then took me back to the Utilities page spontaneously. It didn't give me an alert or an error of any kind. It has done this multiple times. I may try Migration Assistant and see how that works. I know that a 4-year old MacBook is a bit of a dinosaur anyway, but the machine has been very useful and powerful for the whole time I've had it, and this is not how I'd like to see it die.

I also have a lot of important data on the Time Machine and fear that whatever afflicted my MacBook may afflict the MacBook Pro I intend to get soon, which I will load my TM onto.

Any and all help is deeply appreciated.

-Sam Taylor