To elaborate a bit on Niel's advice:
The iPhoto application you have currently installed is associated with the AppleID that has been used, when the Mac has been set up. Since it is impossible to change the association of an application with the Apple ID, you have to delete it and buy a copy of iphoto using your current AppleID, if you cannot activate the old AppleID again.
iPhoto is now listed as free on the main page of the AppStore.
- Delete your copy of iPhoto, but don't empty the Trash.
- Sign into the AppStore with your current AppleID (The "Store" menu in the AppStore app),
- Then go to the main "Featured" tab of the App Store and enter "iPhoto" into the search field and download it.
Be sure you have a current backup of your iPhoto Library, before you run the new iPhoto version the first time. The iPhoto library will beed to be upgraded to a new format, and that can sometimes go wrong, if iPhoto crashes during the upgrade. Check, if you have plenty of free storage on your system drive.