Thank you to Steven who did show that the problem in fact was that I had an alias defined on my network drive that was causing the service to fail to start. The Wampserver tray menu would not let me delete that alias because the service was not running, so Steven went into the wamp\alias directory and removed the offending file. Then the service came up fine (albeit without my alias).
Presumably the reason is that you don't want your server to be able to access network resources (for security reasons I suppose). While that makes sense in general, in my case it doesn't.
Interestingly, when I started Apache manually myself it had no trouble getting access to those files. And I even tried to configure the service to log on as me (and a separate dedicated account as well) but no luck there. He did send me to a page: [
httpd.apache.org] where about halfway down they talk about enabling the service to be able to access network resources. Unfortunately it was written with Windows NT, Windows 2000, and even Windows XP (but I assume Professional). The instructions were definitely not applicable to Windows 7 Home that I am using. As of now I am trying to map their recommendations over to my system but have been unsuccessful. At any rate, that's what the current issue is, not with wampserver itself. If I make any headway I'll inform here, but for now that's where it stands.