I get weird tray failures in KDE sometimes, too. It's usually because some process which was attached to the tray failed (in this case, GAIM, but for me it's often mail-notification), and screwed up some unrelated tray icon (in this case, the language indicator, for me it might be firefox running with alltray).
I would suggest opening KDE System Guard and using it to kill any GAIM and Language Indicator instances that may appear. You might be surprised to see a gaim instance running, but certain crashed applications often leave a zombie process behind. When this happens, the program is still considered to be running by the system, although it isn't running to the user perception.
Since KDE may very well be set to restore your previous session, this zombie process will be re-run even after a restart, so kill it. Then restart the Language Indicator; hopefully it will appear. Then you should be able to start GAIM and have it run normally for as long as it does before it crashes again (if it does).
Hope this helps.