Finally got my hands on the laptop and tried the things linked from this thread (both by me and others)...

- Update the driver:
Newest generic driver from Synaptics: refuses to install.
Driver from Toshiba's web site: Same driver as what's already installed.
Let Windows search for a newer driver: Cannot find a better driver than what you've already got.

- Change the button mapping: The option they say doesn't exist on my screen. They say that under "buttons" there should be something that says "Scroll", and nothing says that, there's just left button and right button.

- Edit the ini file in the Synaptics folder to add a "Mozilla" section with certain values underneath it:
That section and those exact values are already there.