iphoto library won’t open and backup is on an external hard drive

Is the iPhoto library on your external drive one that you manually copied the iPhoto library itself onto that drive from your old computer? Or is your external drive a Time Machine backup of your entire old computer?

You can select your photo library on your current Mac if you hold down the Option key when you open Photos and it lets you choose the library, which you can point to one on an external drive.

If your photos are part of a Time Machine backup on your external drive you can use Migration Assistant App on your current Mac to import data off of that Time Machine backup.

Restore your back up - after all, that's what it's for.

Repair your Library: Download iPhoto Library Manager and use its rebuild function. (In early versions of Library Manager it's the File -> Rebuild command. In later versions it's under the Library menu.)

This will create an entirely new library. It will then copy (or try to) your photos and all the associated metadata and versions to this new Library, and arrange it as close as it can to what you had in the damaged Library. It does this based on information it finds in the iPhoto sharing mechanism - but that means that things not shared won't be there, so no slideshows, books or calendars, for instance - but it should get all your events, albums and keywords, faces and places back.

Because this process creates an entirely new library and leaves your old one untouched, it is non-destructive, and if you're not happy with the results you can simply return to your old one.