Changing file permissions was critical
Thanks for the information and the attachments xjarl!
This worked perfectly for me, but only after I changed the permissions on the 3 files! I bought a Coolpad (Yulong) 8022 with Android 2.3.7 in China through China Mobile. I rooted the phone but was unable to install Google Play until I found this post. I downloaded the attachment, extracted the files and copied the 3 APK files to my system/app folder and rebooted. After installing Google Play and running it, I could browse all the apps in the store but I could not download or install them. The progress bar didn't move.
So I launched Root Explorer and went to the system/app folder. Then I changed the permissions of the 3 APKs: GoogleServicesFramework.apk, GoogleLoginService.apk and Google_Play-v3.8.17.apk to rw-r--r-- to match all the other files in the folder and rebooted. Since then everything has been working fine! Now I can browse the App store and download and install files without a problem!
So, the steps I recommend are:
1. Root your phone.
2. Download the attachment above.
3. Extract GoogleServicesFramework.apk, GoogleLoginService.apk and Google_Play-v3.8.17.apk from the RAR file and copy them to the system/app folder on your phone with Root Explorer.
4. In Root Explorer click Mount R/W. Change the permissions of the 3 files to match the permissions of the other files in the folder (rw-r--r--). Then click Mount R/O and exit Root Explorer.
5. Reboot your phone.
6. Go to Accounts & Sync in your phone's settings, click Add account and enter your Google/GMail account details.
7. Go to your apps and Launch Google Play.
I'm guessing that this will work on any Android phone. Good luck!