however, I cannot remember my password!
If you don't know the admin user account password, that's a problem. That's essentially a separate problem, probably more serious than not being able to launch apps. You need that password for many things, including installing new apps and changing system level settings.
It does not work to simple copy the Applications folder to an external drive, because some apps have required components at other locations, such as in the Library folder. Some apps install system extensions. The only reliable way to back up your startup disk is to back it up completely, not piecemeal.
I asked which version of Mac OS X you are using... If it's Leopard, you can back up the entire startup disk using Time Machine to a backup archive (on the external drive), which you can later use as your data source for "migration" into your new system. Or, if it's Tiger (or Leopard), you can use the built-in Disk Utility (while started up from a Mac OS X installation disc) to duplicate the startup disk to the external drive (or create a disk image file of your startup disk). However, there's a problem, if you don't know the user account password. I don't think you'll be able to use the automated Migration Assistant process to migrate your apps and data to the new system, if you don't know the password for the user account you are migrating.
You should definitely back up your user data (the files in your user account home folder). You can also back up your apps; some of them are drag and drop to install. Install a fresh system and restore your user data. Then, try to restore your third-party apps (one at a time), but for the ones that don't work, you'll need to reinstall them completely from their original source.
(Write the admin user account password down and keep it at a secret location, so that you do not forget it.)
