It sounds like the designer of the program has limited your Privileges to prohibiting the export of records. Personally, I find that unacceptable: it is like saying that 'I own this program' (which is perfectly acceptable) compared to 'I own your data as well' (which, to my mind, is absolutely not acceptable)
You could contact the providers of the program and ask them to give you access to export all or your data.
If you can print a report or layout with the data you need, and can view all records, and print currents records and print to a pdf, you may be able, with some effort to capture your data.
Contacting the person that took your money for the database would be the best solution.