The courts do not get involved in these types of cases regarding educational facilities and testing or grading or even quality of classes. The courts use the phrase that they "will not stand in the shoes of the educational facility" to make these decisions, which means there would be no case law to help you. The courts only get involved when there is some violation of the Americans with Disabilities Act or some other form of unlawful discrimination in the education process.
If you were allowed 3 hours for the test, but were only given 2 hours, this is one argument you can raise with the professor. Second, you need to go to the testing center, hoping the clocks are still off from one another by 10 minutes and try to get a picture of both clocks with your cell phone (if not, do not worry about it). Finally, in your letter you need to outline the facts, leaving out the part about the questions you knew and did not know etc. Stick just to the facts regarding timing and that you were pacing yourself by the clock you could see and you could not see the clock that was behind your back. Explain how you were answering on the exam sheet and would have had plenty of time to transfer the answers to the computer sheet had the clock you were watching been accurate or had you been given the full 3 hours for the exam that you were supposed to have been given.
Typically the facts themselves in these cases will work with a reasonable instructor.
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