You can go into a computer store and see if they can somehow recover the backup files. Without those there is no memory of what was before.
What exactly do you mean by "My computer crashed" and what did you do to get it back up and running?
By default LR stores the backup in a subfolder called Backups in the same folder as the catalog file. This is bad because if the drive that holds the catalog file fails all your backups are lost just like the real catalog file. So it is up to the user to select a different drive to store the LR backups.
Also you should have backups of your complete system because every computer will fail at some point.
After exporting pics, LR and my computer froze up and was non responsive. I had to restart my computer and when I opened LR, none of my edited pics were there. I attempted to restore from the backup, but found there was no backup. I now only have the pics that I had exported. I had 2,000 edited pictures that are now gone.
... and when I opened LR, none of my edited pics were there.
Is it possible you opened (accidentally?) a new catalog file? Go to File->Open Recent and select each of the catalogs listed there to see if you can find the version with your edits.
I attempted to restore from the backup, but found there was no backup.
This really doesn't explain anything. A computer crashing and then getting restarted will not cause backups to disappear. You should use your operating system's search feature to search backups of your catalog file. If you are using LR 5 or earlier, the backups have names that end with .LRCAT; for LR 6 and LR CC 2015, the backups would have file type .zip, and when you unzip the file, you will see .LRCAT files.
Have you searched your computer for the images? They are not IN LR. LR is just a database system and no images are ever stored Inside LR or the LR catalog file. So search your computer for the images you think are missing (they might be missing from the current LR catalog file you have open in LR but more than likely they are on the hard drive someplace).
Also search for LRCAT and LRCAT.zip. LRCAT is the file extension for LR catalog files and LRCAT.zip is the file extension for LR catalog backups.