It depends on how the link in the taskbar reads. If the new version has the same path as the old one, your taskbar link ought to be OK, but it sounds as though your new version got installed to a different place, in which case you wouldn't be able to open it with that taskbar item.
The default directory that OpenOffice.org uses is /opt/OpenOffice.org1.1.3. That's where I let it put mine.
You're supposed to go as root into the "install" directory created when you unzip and un-tar the file you downloaded from
www.OpenOffice.org, and enter "install" which does the initial installation, then go back into that install directory, still as root, and do "setup -net." That sets up the main files.
Then if you haven't used OpenOffice.org as a non-root user before, you go into the /opt/OpenOffice.org1.1.3/program directory and, as the ordinary user (not root) you do "setup" pure and simple, which creates your own files in your non-root home directory.
But you HAVE been using it, so you surely already have all those files, and you don't do this last part. Instead, OpenOffice.org1.1.3 will recognize and use them, as long as you've deleted that file I mentioned in the other post.
As far as starting the program, if the taskbar link doesn't do it (and I'll bet it won't), you can go into a console as ordinary user and type "soffice &" and that will start it up (in the background, so you won't accidentally kill it next time you use the console). Then you just need to find out how to change your taskbar item to point to the right place. Without knowing what window manager or desktop environment you're using, I can't help you there, but it should be a simple thing to do if you poke around for how to do it.