iMac applications restored from back-up are not opening
Are you running the program from the backup HD directly, or did you do a Migration Assistant (the latter would be better, its located in Utilities).

Also, your photos are in /Users/(you)/Pictures/iPhoto Library.  As long as you have this folder, your photos are not lost.

The next step is just to install (or update) and get iPhoto working again.  Try to install from your CD (if you have any) or app store.  As soon as it is working again, it will be able to find your pictures in the above folder on your new Mac.