With your old hard drive in another PC, you won’t be able to just log in and click on My Documents and expect all your files to be there. Instead, you will have to manually locate them or run a search.
In Windows XP, remember that your data such as the My Documents folder is typically found under \Documents and Settings under the username’s folder. In Windows Vista, your user data is stored under \Users. Other program data depends on the software you are using. You may even have to go so far as to install that software on the spare PC just to see what the default folder name and location is for where it saves your data.
Once you locate your files, I highly recommend that you take the time to back everything up to a CD or DVD, or even a USB flash drive. Since you will likely be in the position of having to reconfigure your PC or even buy a new one, it would be the perfect time to make a backup of all your data. In the future, you should make a habit of regularly backing up your personal data.