If the machine is running IE 6.0, then it really should be upgraded at least to 7.0.
Version 6.0 is buggy and no longer supported for security updates.
Though 8.0 has significantly more security features, I still use IE 7.0 and find that it runs better on my older and lower resource machines.
Version 7.0 is still supported for security updates, but I suppose sometime soon, I'll have to bite the bullet and upgrade to 8.0
I use Firefox 3.6x for most all browsing, and IE only for Windows and MS updates, and a couple of government sites.
This discussion raises the issue of eventual inevitable solution for this machine…. which may involve a fresh installation of the operating system and drivers.
You "may" be able to solve the immediate 0xc000012d by updating your video/graphics driver (particularly if it is nVidia brand.
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Unhappily, we do not know what method the school system used for installing the operating system and drivers.
They may have used the machine as an incorporated part of their Network, and may have deployed OS and drivers accordingly.
But maybe you will be lucky and find that your version of Windows does have an individual Product Key (25 digit alphanumeric code)
Have a look on the outside of the case, usually on the bottom, or possibly inside the compartment for the main battery.
If you find the holographic MS Product Key Code Sticker, then all you may need is the matching installation CD
It's also the case that if you eventually re-install the Windows Operating System, you will loose all of the installed applications, including MS Office if that is installed.
Again, you may be able to discover the Product Key Code, this time by using
Belarc Advisor
It is always handy to have a print-put of Belarc Advisor for any machine, since it lists your Product Key Codes as well as identifying information about all of your hardware.
But my meandering thoughts may be taking you way beyond what you wanted to get involved with.
If your machine is functioning as you wished at this point, then we can take a break and resume any larger scale plans at such time as you prefer.
Best Regards