Ok, so I assume that you're not living with your parents, and you want to connect to them over the internet, right?
I'm doing something quite similar to what you want to do, but my experience has been with RealVNC instead of TightVNC. I imagine the concepts/procedures are more or less identical:
1) Yeah, you'll want to assign your parents' XP box a static IP on their home network.
2) Make sure you've installed the vncserver software on the XP box. I know RealVNC has one for XP, I assume TightVNC does too.
3) Set up your parents' router to forward incoming requests on the appropriate VNC port to your parents' XP box. For RealVNC, it's usually in the 5800 and 5900 ranges. You don't mention a specific brand of router, but I've done this successfully with 2 different Linksys routers and a D-Link.
4) If Ubuntu doesn't come with an instance of vncviewer, you should be able to download the appropriate version from the TightVNC website.
5) Once you've got vncviewer running on your Ubuntu box, you should be able to simply type in your parents' URL, and you "should" be able to connect.
I would first make sure you have no problems starting vncserver on your parents' XP box and running vncviewer ON that box just to verify that vncserver IS running.
(BTW, SSH IS more secure, and you can pipe VNC traffic through SSH, but that's another topic
)
Hope this helps a little