Ooohhh. The mis-information and helpfully wrong suggestions in this thread are painful. Here's your situation:
1. Your cat helpfully killed your computer in the middle of some sort of important write to a windows system file or the registry or some such. You could have probably fixed this using your original install disk and doing a repair install.
2. Your HP Restore move quite helpfully laid a fresh install of Windows XP down on top of the burning rubble that was your old XP install, wiping out your old registry and all its useful info about your installed applications, etc. And almost certainly also wiping out any relevant system restore info which could also have saved you.
3. As you have discovered, all your old files, folders, and applications are intact. Your windows install simply doesn't know about your previously installed applications. Your hard drive is fine for the moment (always excepting your cat) and your personal files and data are in no serious danger. (Unless you have blackmail material on said cat.) So any suggestions for data recovery services, etc. are pointless. Similarly, call to your local favorite Geek Dogs on Call computer repair service will prove similarly unhelpful and will likely only result in a recommendation that your computer needs more RAM and/or a formatted hard drive with all your data truly lost.
4. So now to the actual solution. As suggested, your only option is to painstakingly hunt down all your application CDs and reinstall them. The files in your programs directory are only particularly good for running and uninstalling the applications, not reinstalling them. The one exception is if your computer originally came with office installed on it by HP. If so, you might find the necessary install files in C:\i386 or some other cryptically named folder. If you can't find the CDs, you're stuck with buying new copies or trying out the
free, open-source equivalents.