If the Aperture library was on the internal disk that was replaced then the only way to get the library back would be from any backups you have of it.
In a situation like yours the originals are stored on the external but all the adjustments you made and metadata you added are kept in the library and if that library was on the internal disk it is now gone.
Sorry to have to tell you this. At least you have the originals. Please take the time now to setup and begin using some backup plan.
And make sure you make a copy of the external drive as soon as possible. Drives die (as you found out) and if that external goes you will loose your originals!.
Restoring my internal drive was lengthly and convoluted. It seems time machine was not doing what I had set it up to do. Even now when I go back to before the crash the dates are there but there is no way to open that date. The store did not make a back up because time machine said it had done a back up. I still feel, however, that there is a backup somewhere. I am just not aware of how to look or find it. With my photos, I was always worried that I would loose them so I made sure photos were on the external hard drive. I just never made sure all the versions were. Not even sure how to do that. If I can't resore my library with all the versions, how do I at least get the masters back into Apeture?