Actually, yEd should be backwards compatible (i.e. you should be able to open your older files). The only known exception is diagrams created with yEd 3.4.x that have embedded SVG documents which use SVG 1.0 elements that have been removed from SVG 1.2.
To be able to help you, you need to provide more information. What version was your previous yEd installation? What happens when you try to open older files? If there is an error message, can you please post that message here and upload the corresponding file? (See How to upload files to yEd Q&A? for instructions. Please only upload files that do not contain confidential/sensitive data.)
