How many times should the computer cycle on-off when doing a factory reset?

Question

I have a Toshiba A665-S6065 which can not boot.  Yesterday I tried the Auto Recovery by holding the 0
while booting, and following the default instructions.  It seemed to complete without errors.  But the computer
will still not boot.  Today, when reading the instructions, it said to expect the computer to cycle on and off severa
times.  So how many times?  will there be any propmts or messages?  How long should the entire process take?
How long should the computer be off before it turns on again each time?  I think I might be screwing things up
by intervening and trying to start the computer myself because it isn't clear to me what should actually be happening.
Could someone please tell me what to expect before I start looking at possible hardwre problems?
BTW, I can access the Setup and Boot Menu.
Thanks,
kjdroid 
NEW info:
Now when I boot while holding the 0 key, instead of going directly to the Recovery Wizard, it goes to the
Windows Boot Manager.
from there the options are Windows Setup [EMS enabled]
and Windows Memory Diagnostic, as well as the F8 option for advanced options.
If I select Windows Memory Diagnostic I get
File: \boot\memtest.exe
Status : 0xC000000f
Info : The selected entry could not be loaded because the application is missing or corrupt.
If I select Windows Setup or F8 followed by normal windows startup or startup in safe mode then
I get the following sequence of events.
Starting Windows with the Windows logo.
then the blue screen
Then to the Toshiba Recovery Wizard, where it partitions, and does the CRC and then prompts to press
finish to restart the computer.
Either the computer does not shut down, or it stops and starts very quickly because all the lights cycle
on and off but it does not appear that the start/stop light actually ever turns off.
Then I get the Starting Windows with Logo again.
Then the Recovery Wizard comes back but only with the screen about partitioning.  It does not
do the recovery and CRC this time.
Nextis the Toshiba Logo reappears again with the options for F2 or F12 for the Setup and Boot Menus.
Finally, I get a blue screen and it appears nothing else is happening.  I let it sit for 30 minutes before I retry, because I am not sure what is supposed to be happening now.
Also, one of my attempts, I got as far as the messages:
Setting up the Registry
Starting Services
Applying System Settings
Will continue after restarting your computer
Is preparing your computer for first use.
But then again, it just goes into the blue screen state until I finally decide to shut things down.
Am I being premature or should I let the blue screen sit there for a few hours while work is being
done in the background?  I don't hear any sounds from the computer that would indicate any type of activity.
Thanks again
kjdroid

Answer 1

Actually, it's kind of hard to tell you what to replace. If you have a spare hard drive laying around, go for it. It also could be memory issues (I have the same model as you) & it was my sister-in-law's notebook before I get it. The notebook had several memory dumps that CCleaner found & deleted when I was working on it. 
I told her that I would re-install it for her to make sure there no viruses or such. After backing up the computer, I proceeded to what was supposed to work, pressing "0" at startup to no avail, then booted into the area where the system restore, command line repairs & such were, & there was the option for a factory reset, the last option. I chose that one, & like you stated, it rebooted numerous times, until finally it was through. Longest factory re-install I've ever done. 
What led me to believe there were memory issues was during the first round of updates, it BSOD'd, another memory dump was found by my portable CCleaner. It still had the original Samsung PC3-8500 memory, so I took the memory that shipped with my MSI (PC3-10600) & installed that, then not only was all fine, it was noticably faster. Once I got it fully updated & scanned with MBAM & the ESET Online Scanner (I always do this when installing or re-installing a computer), I removed my memory & placed hers back in, then returned it to her. 
I ended up with it about 10 days later, she said it was still dumping. Needing a spare notebook, I offered $100 for it, ending up paying $150, but still came out way better than on eBay. 
Once I got it, I placed the 6GB RAM back in there that I had, & also replaced the HDD with a extra Crucial M4 that was laying around. Right before swapping drives, I ran HD Tune (free) on the original, there were yellow attributes, meaning that it had issues pending. It's a 500GB Seagate HDD that runs at 7200 RPM. Just so happened, I lost a 500GB Seagate Barracuda desktop HDD (7200.11) less than a month ago. Booted the computer, the screen stated "No Operating System found". 
So it could be either the HDD or memory (RAM). Or worse yet, the MB itself. Has it been dropped? Notebooks are fairly durable, but they don't take to being dropped very well. Does it run hot? If so, there may be severe dust buildup that's causing it to overheat, that will make it BSOD. My guess is that's it's one of the first three that I mentioned above & if it's the MB, forget it. Prices are too high, even for used ones & in a notebook, it's basically a total teardown to replace it. If it's a new MB, it may cost between $200 to $400, depending on popularity of the model. That's too much to pay to repair a computer built in 2010. 
I'm trying to give some suggestions here, based totally on personal experience on my & other's computers that I work on. However, online it's a cat & mouse game. I don't want to tell you to purchase another HDD unless it's almost 100% certain that's the issue. Which is why I asked if you have a spare earlier. Also, try reversing the position of your memory sticks (a 5 minute job), it's behind that lid close to the battery underneath the notebook. 
Post back if you need further assistance. Someone else may have other ideas, so follow the thread.
Best of Luck,
Cat