It crashes because you downloaded and installed a driver direct from AMD. Graphic card drivers are created by the chip manufacturers (AMD/NVidia/Intel). These drivers are, for lack of a better term, Generic drivers for any particular graphics card. Laptop manufacturers will take those drivers and tweak them to limit the power draw and heat ceilings to conform with the specifications of the laptops they install the chips in. As an example (and just throwing out numbers. These are not actual figures):
The AMD 560m mobile graphics chip (don't know if that's even a thing).
Let's say it has a TDP of 26 watts and on full draw, heats up to 97 degrees.
Now lets say that Toshiba wants to install that graphics chip into one of their laptops, but 97 degrees it too much heat for the cooling system to handle. So Toshiba tweaks the driver to limit the power draw down to 22 watts and the graphics chip never heats up to more than 85 degrees.
Now you install a new driver direct from AMD and those power limitations are gone. Your system starts to overheat and Windows starts giving errors. It's even possible that the overheating could have damaged some components.
Not saying this IS what happened, but it is a possibility. Also, when you reinstalled Windows, did you use Windows 7 from the Toshiba Disk Creator or a generic Windows DVD/ISO? Same thing here could happen. Generic Windows 7 can cause issues just like generic drivers from AMD.
I understand where you're coming from, but from what I'm seeing, the system came with Windows 7 and should be able to run it (possibly tweaked by Toshiba) without a BIOS update. Additionally, a BIOS update only resolves whatever specific issues are listed in the BIOS update notes. If Toshiba has not listed a new BIOS version that specifically states it resolves a graphic card issue, then one does not exist. Anyone claiming otherwise should need to provide undeniable proof that it works on your exact model number before making any changes.
My recommendation here would be to get a reinstall disc from Toshiba and perform a clean Windows 7 install (this may be at a cost). Next, download and install the latest drivers from the Toshiba web site. If this is done correctly and you're still running into issues, I'd contact Toshiba directly and see what they have to say.
-Wolf sends