Get into the BIOS with out the docking station.
Then Ctrl-F7 while in the bios. Also make sure for some reason the BIOS has not been reset or changed and check the display options settings, there should be options for outputs.
If that doesn't work, you may be right and would have look into replacing the motherboard.
If a replacement motherboard is expensive for your model (bluetooth, fingerprint reader etc.Lenovo has many sub models of the T60 line ) you could have the graphics card issues repaired at a hardware level with a professional shop.......or look into getting a used replacement motherboard, again this can be difficult finding the correct one.
Places that sell used MB online are usually helpful and should be willing to help you make sure it's the correct one. If going to all this trouble finding a motherboard, finding a faster processor etc......shouldn't make much of a difference in cost if that is something that would interest you.
If the BIOS options do work, and you get the external display to work, you could remove all ATI drivers in windows with the add remove programs and use something like "Revo" un-installer to get rid of anything left over in the system registry (easier then editing the system registry on your own).
Reboot and then use Lenovos update service what ever they are calling it now, to find the ATI drivers for your graphics card from lenovo, their version may work better with your laptop......I don't know which version of windows you are using.
Lastly, if replacing your motherboard depending on your version of windows it may prompt you to call microsoft to enter a new "code" if windows thinks it's been installed on another computer.