Can'f relaunch Finder

[Sdw7 at aol.com]

Need some help, folks--over the last couple of days, I installed OS 10.2 and downloaded all the upgrades from Software Update, so now at 10.2.8 on both Macs. My trusty old B&WG3/350 seems to be OK, as was my wife's iMac G4/800/15" flat screen (both 768 MB RAM)--until tonight, when applications began to quit unexpectedly on the iMac. 

I tried to Restart, but it wouldn't log out, then I tried to use Force Quit--and ended up with many, many entries for the Finder. Repeated use of Relaunch did nothing, nor did it seem to even shrink the list. That keyboard has no power switch, so I tried the computer's power switch. Each time, it simply returned to the Force Quit window with all the Finder entries. Nothing in Mac Help comes close, and nothing in this or a couple of other Listserv archives does, either. 

Anybody have any ideas? Many thanks in advance.

Steve in Raleigh