You took the hard drive and put it into a spare desktop that didn't have a drive in it - is that right ? I am surprised it ran at all as the driver set would be different, particularly the chip-set drivers.
By all means, add it as a second drive to a working desktop, or slave it by a USB connection (requires a 'caddy') to any computer to recover your data from it, but for the repair, I'm not clear on what you mean.
If you mean repair the laptop, once a new mobo is fitted the hard drive should work perfectly well. It may need the drivers replacing, but these should come with the motherboard or be downloaded from the Toshiba web-site.
If you mean continue using the Toshiba hard drive in the desktop, but have it working properly, you need the drivers for the hardware that is in the desktop, particularly the chip-set drivers.. The mobo in the dektop should be marked with the maker and model number. You need to go to their web-site and download the Win 7 drivers for it. A memory stick and another computer would be the best method for this.
If there is a problem with the Win 7 installation on this hard drive, the Windows install disc would be the best method to repair it - do a 'Repair install' - and if asked for an authentication code - the COA - use the number off the desktop.
If you are going to put it back in the Toshiba, then again use the Windows disc and the COA off the Toshiba. You will need to make a phone call to MS to get it authenticated as a new mobo is considered a new computer. If you decide to use the Toshiba recovery discs this will restore the laptop to an ex-works condition and all your data and applications will be lost and you will still need to phone MS.