I am afraid I am finding it difficult to understand what is happening.
Is your iPhoto library present? If so maybe you don't need to restore it from Time Machine at all ( but restoring it from TM shouldn't ask you what application to use)
http://support.apple.com/kb/HT2604 tells you how to re install iPhoto.
The HP photo app won't be able to see any photos in your iPhoto library.
mike...thanks again... i went to the link....but i did not get any installation cd with my mac. guess i need to take it to a repair shop !! but thanks so much for taking the trouble..and giving your time. And I would really appreciate it if you let me know any other way, if its not too much trouble..
thanks a lot, once again.
I guess that link was written before Lion and the App Store came into being.
Try googling "reinstall iphoto lion". you will get a lot of hits and can read up and choose the one that applies to your situation.
I assume you have tried just rebooting. I have never had an app become "inactivated" on a mac. You may not need to reinstall the app.
this is what i get when i try to open iphoto:
Process: iPhoto 
Version: ??? (???)
Build Info: iPhotoProject-628000000000000~3
Code Type: X86 (Native)
Parent Process: launchd 
Date/Time: 2012-01-30 00:38:07.875 +0400
OS Version: Mac OS X 10.7.2 (11C74)
Report Version: 9
Interval Since Last Report: 78109 sec
Crashes Since Last Report: 15
Per-App Crashes Since Last Report: 14
Anonymous UUID: 5390C335-FDA3-44B5-8107-0490731B64C2
Crashed Thread: 0
Exception Type: EXC_BREAKPOINT (SIGTRAP)
Exception Codes: 0x0000000000000002, 0x0000000000000000
Application Specific Information:
dyld: launch, loading dependent libraries
Dyld Error Message:
Library not loaded: @executable_path/../Frameworks/Geode.framework/Versions/A/Geode
Referenced from: /Applications/iPhoto.app/Contents/MacOS/iPhoto
Reason: image not found
0x1000 - 0xd1afeb +iPhoto (??? - ???) <68601E93-E4CF-3B4C-AFFD-4781A92DD58B> /Applications/iPhoto.app/Contents/MacOS/iPhoto
0xe83000 - 0xf63fe7 org.python.python (2.6.7 - 2.6.7) <61DBA92A-C39A-3A52-86F2-59CF9D310CB4> /System/Library/Frameworks/Python.framework/Versions/2.6/Python
0x8fe23000 - 0x8fe559c7 dyld (195.5 - ???) <134323A7-49DC-3A9D-ACFD-32FAD0FD6BA2> /usr/lib/dyld
Model: MacBookPro8,1, BootROM MBP81.0047.B24, 2 processors, Intel Core i5, 2.3 GHz, 4 GB, SMC 1.68f98
Graphics: Intel HD Graphics 3000, Intel HD Graphics 3000, Built-In, 384 MB
Memory Module: BANK 0/DIMM0, 2 GB, DDR3, 1333 MHz, 0x80CE, 0x4D34373142353737334448302D4348392020
Memory Module: BANK 1/DIMM0, 2 GB, DDR3, 1333 MHz, 0x80CE, 0x4D34373142353737334448302D4348392020
AirPort: spairport_wireless_card_type_airport_extreme (0x14E4, 0xD6), Broadcom BCM43xx 1.0 (126.96.36.199.18)
Bluetooth: Version 4.0.1f4, 2 service, 18 devices, 1 incoming serial ports
Network Service: Wi-Fi, AirPort, en1
Serial ATA Device: Hitachi HTS545032B9A302, 320.07 GB
Serial ATA Device: OPTIARC DVD RW AD-5970H, 1.27 GB
USB Device: hub_device, 0x0424 (SMSC), 0x2513, 0xfa100000 / 3
USB Device: Apple Internal Keyboard / Trackpad, apple_vendor_id, 0x0246, 0xfa120000 / 5
USB Device: BRCM2070 Hub, 0x0a5c (Broadcom Corp.), 0x4500, 0xfa110000 / 4
USB Device: Bluetooth USB Host Controller, apple_vendor_id, 0x821a, 0xfa113000 / 6
USB Device: FaceTime HD Camera (Built-in), apple_vendor_id, 0x8509, 0xfa200000 / 2
USB Device: hub_device, 0x0424 (SMSC), 0x2513, 0xfd100000 / 2
USB Device: IR Receiver, apple_vendor_id, 0x8242, 0xfd110000 / 3
I think you need to take it in. Too difficult to understand and resolve like this.
As I said before your photos live in the iPhoto library, so provided that is still on your machine in your user/Pictures folder, you should be able to get to them again when you have sorted out iPhoto.
Have you tried double clicking on the iPhoto Library? Does iPhoto just crash as above?