Hmm. How do you normally back up your data files?
I should have been clearer. You don't need any special backup application to do the job (though you probably should be using something on a reasonably regular basis....).
A couple of ways of doing the job.
First, starting with a terminal from your home directory:
cd .mozilla/seamonkey
tar -cvzpf /path/to/a/directory/seamonkey20100223.tgz .
For this, you need somewhere that you have write permissions to put the archive that you create. I have a directory /home/stor/backup which my normal user ID has write permissions for, which is where I would dump that sort of file. The switches used on tar are as follows - c (create) v (verbose) -z (compress using gzip) -p (preserve original permissions) -f (file, followed by a space and the name of the file to create). The trailing dot (.) on the command tells tar to start from your current location. I always tend to date my backup files (hence the 20100221 in the filename), so I have some idea how current they are.
Another easy way to make a one-off backup is to use MC. Open it using 'mc' from a terminal, navigate to .mozilla/seamonkey (enter the seamonkey directory) then press F2. You'll find an option (its number 3 on my menu, may be different depending on what version of MC you are using) which is something like 'Compress the current subdirectory (tar.gz)'. Press that number. It will prompt you for a file to create (and tell you not to include an extension). Enter the full path of where you want the file saved and a filename (without extension

) and press return.
That will create an archive with all your profile details and mail (if you use Seamonkey as a mail client). What it won't do is allow you to exclue files, so it will also backup the browser cache, which is a bit unfortunate.
You can then delete the ~/.mozilla/seamonkey directory and the directories below it (be careful to
only delete seamonkey and below, not any of the other directories in .mozilla. Next time you start (or attempt to start) Seamonkey, it will create a new directory and create a basic profile for you in that directory.
If that does solve the problem, you will still have some problems, since there is no easy way to migrate things like passwords to the new profile. You can always use MC to retrieve things like your bookmarks, but the passwords are stored in encrypted form, so you will need to know what they are.
If you find it doesn't help, delete the new ~/.mozilla/seamonkey directory and use MC to restore the copy you made.

Its late and I've been working for the last 12 hours, so I hope this is clear. If not, I'm happy to try and answer any questions, though its going to be after I've had a few hours sleep....
Paul.