I am having a very similar problem.. All of my apps unexpectedly quit when I try and open them. Im on 10.3.4. This just started happening to me 2 days ago. I think it happened after a power failure, or 2 in a row (i have my surge protecter plugged in where the chord can easily be pulled, not by choice but its the only available situation). This may or may not be the case.
After it happened to me the first night i Pulled my hd out and put it in my old beige g3 (forgetting that the beiege g3's dont support 10.3 without xpostfacto installed from os 9), and then today I got the HD back on the original machine, and it was working. I have no idea why this could have happened. Tonight i cam into my room and there was the error on the monito saying I HAD to restart my computer right now. I hit ctrl-apple-restart several times on the keyboard and nothing happened. The computer im using doesnt have a restart button (old imac 266), so i had to flip the switch on the surge protecter to restart it. When I turned it on again I started having the same errors again. I just dont get it. I also cant find my disc warrior 3 cd which i somehow manged to lose while attempting to fix my beiege g3.
Oh when will this end?!?!