Is your entire system up to date? Have you reloaded in Synaptic, marked all upgrades, apply (twice) and let it do everything? We can't help unless you have done that. Run konqueror in a terminal, as in Konsole type konqueror and hit enter. Now it will give error messages. Post those here. Will konqueror run in root? Log in to root and try it. If it runs there your system is OK. You may have a problem in your home account konqueror config file. You could rename the konquerorrc file in .kde/share/config, with konqueror not running, then run it and let it create a new rc file. If that works you can reconfigure konq as you like.