The Installer (OS X) DVD not the Applications DVD. No you will not lose your apps or settings because you are not going to actually install an old copy of OS X on top of the latest one you just upgraded. When you boot up with that OS X DVD in charge, you'll have to choose your language, then it gets to a screen that is ready to begin the install. It also has some instructions on there about choosing options from the "utilities" menu. That's (later option) is what you want to do: choose "Disk Utility" from the Utilities menu.
Run "repair permissions" from that. I'm guessing you ran it from Disk Utility in Applications/Utility on your hard drive. That's no good. You have to run the repair with the DVD version of OS X in charge.
After that completes successfully(?), go ahead and run "Repair Disk".
After that completes successfully(?), close disk utility. Then, go back into the Utilities menu and choose startup disk. Choose whatever you call your hard drive startup (probably Mac HD or similar).
Then, restart. That should boot you back into your hard drive install of OS X.
See if you still have the problems.
If so, try the combo install of OS 10.6.5 referenced (by link) earlier in this thread. That will most likely solve your ichat issue if the above doesn't do the job.
Did that solve the problems? If not, repeat the above (using the install DVD, repair permissions (because you just installed a bunch of OS X files from the combo install). See if that solves the problem.
If not, I would consider trashing your iWord applications, reinstalling them anew, then updating them via software update. See if that solves that problem. If not, I would head for the Genius bar at an Apple store.