A well-known "secret" within the Slavic Reference Service is that libraries and information organizations from across Eastern Europe provide full-text access to many of their best resources. Hungary, oddly enough, is one of the best examples of this phenomenon.
Below is a list of a few online databases that offer the full-text feature for their items. Be prepared to encounter some restrictions, however, since copyright laws still apply in Hungary and items may not be available to users outside the country. Give it a try, though, and you may be surprised at what you find.