Thanks for all the help. I finally got it to sync, but there is a new problem. Some apps did not show after sync. I noticed that some were not checked off on iTunes even though I had selected the option to automatically sync new apps.
I generally add new apps directly from the iPad, not purchasing through iTunes and then syncing. I went back, checked apps and synced again.
Now, when I go to the iPad, it shows a number of the apps need updating, even though I had previously updated them on the iPad.
Did I miss a step? Are apps still not quite in sync?
I think that if you update the apps in iTunes and synch again you should be okay.
I think that this might have been the answer. I don't have an iPhone, so maybe there is a similar step for that device that everybody knows about.
When I deleted and tried to reinstall a free app, I got the message, "You have already purchased this app. Check for available downloads" in iTunes. I think this is a pointlessly cryptic message.
I normally purchase apps directly through the app store app on the iPad. I thought that selecting the option to transfer purchases to iTunes would take care of things when I connected to my PC.
But I noticed an option in iTunes for apps, Check for updates." I selected this option, and let iTunes update before syncing again.
This appears to have worked, although I am still showing a couple of apps that still show as requiring an update.
This may help another user in the future. Note that I don't think that doing a reset accomplishes anything unless you have tried to update apps.