The best way to gain access to your old USAA records would be to contact their customer service branch personally. You name, DOB, and SSN is adequate enough to provide you old records. The customer service associate can also tell you directly if they maintain older records. The USAA main page and subsequent internet sources say policy detail can be granted using basic identification, but in these cases the account is fairly new and active.
Essentially, they will run your tidbits of identity to connect with any existent records. You will have to create a new username and password. If your account is gone they will be able to tell you, if it is still there they can tell you if your eligible. Just because you cannot access your files does not mean you are not eligible. Even if your records can not be located you may still be eligible. You time as a cadet may very well satisfy active duty.
USAA coverage is granted to active or retired military and their immediate families. Your time as a cadet may qualify you for veteran's status, but you will need to contact the Department of Veteran's Affairs. Recent legislation passed after Sept. 11th changed the definition of veteran status. This would mean any time spent as a cadet counts as active service. In this case you would be eligible for full benefits in everything that the USAA covers. However, since your time of service was in the 60's that could cause complications.