Q: no iphoto on new computer

David, did you check the Applications folder? iPhoto may only be missing from the Dock, but in your Applications folder.

What is the MacOS X version on your new Mac?  If it is MacOS X 10.10.3 or later you need iPhoto version 9.6.1.

Your old iPhoto is probably incompatible.

Apple stopped selling iPhoto. New Macs come with Photos instead.

If your iPhoto version is associated with your AppleID at the App Store, Barney's user tip should work, once the App Store is back to normal - there have been a few hickups recently:

See:  Can't Update iPhoto because it is not available in the App Store

Hmmm...does this "Photos" thing replace IPhoto, and if so is it just a case of me trying to figure out how to navigate

Apple stopped the further development of iPhoto and new Macs will come with Photos instead of iPhoto as the basic photo management software.

Sooner or later you will have to abandon iPhoto, when it will become incompatible with newer MacOS  versions.

Photos is very different from iPhoto.

Some background reading:

• Old Toad's User Tip:  Photos 1.0.1 vs iPhoto 9.6.1:  Features and Capabilities
• The Online Help for Photos to get started: https://help.apple.com/photos/mac/1.0/?lang=en#/
• And what to expect, when you open your iPhoto Libraries in Photos:    How Photos handles content and metadata from iPhoto and Aperture - Apple Support

You're welcome.   Good luck, David!