Here at Mr. Transmission on I-10 East, we diagnose engines and transmissions for free. We also have free towing with repairs. Bring it by or give us a call and we'll be more than happy to help you out.
Depends on what's wrong, but generally a shop will charge an hour to diagnose a problem with either, after that hour they should have a good idea as to whats wrong or provide you with a reason to need more time for the diagnosis.