Generally speaking, reinstalling your computer without saving your output style is unlikely to allow recovering the style. But here are a few possibilities to consider:
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If your operating system is post-Windows XP, any modified output style would be kept in a folder in the My Documents section of the computer. If you backed up your My Documents folder prior to reinstalling your computer, the modified output style might still be in a subfolder.
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You mention “reinstalling” your computer. If you did so by using a “restore point” (via Windows), it might be possible to restore your computer to a point pre-dating when the EndNote output style was still present on your computer. This assumes, however, that you designated a restore point at a previous point in time. If you opted to recover the hard drive with an image, the output style could still be present providing it was present when the image was made.
Perhaps other forum users may have other suggestions but looks like you may need to recreate the output style.