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I am sorry to learn about your son's situation.
Unfortunately I do not believe that he has a very good case based on what you have posted.
If I understand the situation correctly, your son initially decided to go to school for the final year, found out about the ban, and withdrew from classes, deciding not to complete his studies at the University.
Your theory of recovery is that if he had known of the ban earlier he could possibly have made a transfer to another university, where he may have received a scholarship.
The problems with this type of claim are primarily two-fold: (1) the plaintiff failed to mitigate their damages (your son was already enrolled in school, but failed to attend school and complete his degree); and (2) the plaintiff's damages are "speculative" in nature (unlike a contract claim, or a general tort claim, the damages here are based on a series of speculations: your son may or may not have been accepted as a transfer student, he may or may not have received a scholarship elsewhere, as you posted in your follow up, most schools are unwilling to provide senior athletes with scholarships).
Damages for travel are not going to be recoverable, he needed to travel to school in any event.
With the above understanding, you may want to try approaching the university and see if you can negotiate a settlement with them so that your son can re-enroll and complete his studies (you say he is trying to get his degree, if that is his goal, work towards that), or some other mutually agreeable resolution. Keep in mind, I am not saying you have "no" claim, just that this is not a very strong claim - so keep your expectations in check (this is especially true if you go looking for attorneys to represent you in this matter - do not spend more on litigation than you can hope to recover in damages). But trying to get the university to reach a resolution to "make it right" is probably something you can do, but expect the negotiations to be flexible on both sides (remember, if your son did leave mid-year, the school had already offered for him to complete his education, he made a decision not to take it, so he is asking for a second chance as well).