It sounds like your backup folder destination has changed. You can go to the catalog settings and change the backup frequency option to "the next time Lightroom exits" and then close Lightroom. On the screen that shows take note of the folder where the backups are being written.
As a side note, you don't need a backup particularly when switching to a new computer. All you need to do is copy your current working catalog to the new computer and use it.
The backup catalogs for LR 6/CC2015 are stored as .zip files.
You need to decompress these files using your OS or other zip software before LR can read backup catalogs.
Go to Catalog Settings and set Lightroom to make a backup every time Lightroom exits. Then when you close Lightroom and the backup dialog box appears, it will show you what folder the backups are being stored in.
Then you can set the backup frequency back to daily, weekly, monthly as you prefer.
I just double checked... the "Show" button you described shows the location of the "Current catalog" only not the backup folder.
It just coincided that backups prior to 2015-4-28 were stored here too.
dj_paige's Instructions below should get you to the current backup folder location.
You can also do that with the "next time Lightroom exits", and you don't need to do any resetting of the backup option.