Can't install Google Play Services
I was able to install Google Play Services by browsing to its page at https://play.google.com/store/apps/details?id=com.google.android.gms and then logging in, clicking install, and choosing my phone.

Come to think of it, I might start installing more apps this way, from the comfort of a desktop browser. :)

Anyway, I'm able to use the Google+ app again.

I'm still puzzled by the "No connection" business and having to periodically downgrade Play to Market to install anything from my phone running Android 2.2, but I'm glad I didn't have to root it and install CyanogenMod as suggested by some friends.