Jim,
This sounds like it could be an issue with your device or carrier (if it has cellular service). Google Play has been around quite a while and I've never heard of any issues getting an app from them. If you would tell us what brand and model of smart device you have and what cellular carrier it's attached to maybe we can continue to help.
Based on this thread, at some point you were getting the message "no new engines" on your tablet so I would assume you had some version of the app working. What changed?
Tony