You can probably find the model number on a sticker on the bottom (or side) or the unit.
I checked out Toshiba Satellite and with most models, they offer a couple of ways to reinstall.
1) Create a set of recovery disks using the Recovery Disk Creator. Go to "Start - All Programs - Toshiba - Recovery - Recovery Disk Creator". This will create a set of recovery disks if (or when) you have a catastrophic hard drive failure. Installing with these recovery disks will overwrite everything on your system, placing it back to factory defaults.
or
2)
Start the recovery process on boot up. This method also overwrites everything on your system, placing it back to factory defaults.
Using either of these methods, you will need to back up all of your data. After the recovery to a "factory" state is complete, you will need to reinstall all of your programs and restore your backed up data.
Since you mentioned that you had the choice to setup Windows 32bit or Windows 64bit when you first got the system, according to
this page, you should be given the same choice when you initiate the recovery process.
Quote:
I've installed a 32bit version of Windows but I would like to change this to a 64bit version (or vice versa); how do I do this?
You may change this by running a System Recovery on your computer. For instructions on how to do this you may go
here.