I am sorry that you are having this trouble with your computer and EndNote.
Currently output styles are not stored in the document so you will not be able to restore the output style from the document.
If you would like to see this feature in a future version of EndNote, You may want to submit a request for a product enhancement on our website.
http://community.thomsonreuters.com/t5/EndNote-Product-Suggestions/bd-p/en-suggest
If you cannot access the old computer at all then output style is lost.
The style would have been saved to your Documents folder. So if you had been using OneDrive or iCloud to back up your Documents folder then you might be able to restore the style from the cloud.
If you need help with recreating the style you can reach out for Technical Support.
Please contact Technical Support directly
1-800-336-4474 option 4 then 1
or
https://endnote.com/contact/
Once again, I do apologize for any inconvenience caused by this situation. If you have any other questions, feel free to get in touch with us again.