joeyjoe, there are extremely good theoretical and practical reasons to think that safely handling bitcoins using a compromised computer is impossible, no matter what tricks you use to protect them, and that this issue is fundamentally impossible to fix. While you can write software which makes stealing bitcoins inconvenient, the only true defenses are (a) keeping your computer secure, and (b) incorporating multiple devices, such as by using multi-signature transactions (coming in a future version).

Various tricks have been proposed for doing protected computation in non-bitcoin contexts, and it always ends up being an arms race with the bad guys having a substantial advantage. Things like using a TPM, hiding the keys behind interprocess communication, in-memory encryption, and device fingerprinting only help a little.

You shouldn't assume that because your teacher hasn't shot you down, that your plan will work. Experts in cryptography often propose schemes that are later proven not to work, and this happens so often that it's considered poor form to advertise anything as truly secure until it's been published and peer reviewed for a fairly long time.