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First possibility is that the hospital or clinic didn't create the CD properly.
Secondly, no insult intended, but you are inserting the CD the right way up? Sorry, but seriously, it happens, believe me. Especially as it only spins for a moment, then ejects.
Third possibility is that it was created for Windows (I'll come back to that).
If we rule out the hospital and the CD is put in the right way up, then you need a DICOM reader specific for Macs. I'm not familiar with the programme you got; but I can say with complete confidence that the Mac-specific DICOM reader OsiriX works perfectly, even if the CD was created for Windows.
I've used this product for many years. Go for the free version - often called OsiriX lite. There is a version specifically for patients. See here:
OsiriX DICOM Viewer | Patients
You insert the CD and it finds the DICOM files and you're good to go.
Don't part with any money for the professional-standard version which is horribly expensive - called OsiriX MD.
Ian