Just an update for anybody who may come across this thread and want to know how things worked out.
Some of the problems returned, even with the 512 MB chip removed. When the original install discs arrived (delayed by hurricane/superstorm Sandy) I ran Apple Hardware Test and got the following error message:
I did a google search for what the code meant and found a forum here:
where someone said it meant that there was a problem with a sensor on the logic board. They said resetting the SMC might help (not sure why). I tried that, ran AHT again, and got the same result.
Though AHT didn't find a problem with the 512 MB RAM, I still think it was contributing to the problems I had with this iMac.
I've shipped the computer back to the eBay seller for a full refund.
Thanks again for all the help from everyone.