iMac applications restored from back-up are not opening My  one year old  iMac failed  to  boot, after   SMC  and  PRAM  reseting  I  got  the  hard disc replaced  and it is working again.

Now  when  I  opened  my  back up,  all  the  applications  were there  but  many of them  including  iPhoto  won't  work  with  error  message  saying  that  it  is  not  compatible  with  the Mountain Lion.

I don't know  how  to recover  my  photos. If  I  go  for  data recovery  will  it be  able  to  recover my  photos  and  can  they  be  viewed  normally  or  only through  iPhoto.
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.