You don't state whether it freezes up while downloading of other apps. I'm assuming it does.
What I had to do when the PlayStore froze(halted) on every download was as follows:
1) force close PlayStore, Play Services, and Services Framework
2) clear data PlayStore and Play Services
3) reboot into recovery
4) wipe dalvik-cache and cache
6) check the PlayStore again for working download
I've had that happen a couple of times when flashing the wrong GApps package or by not doing a simple wipe before and after flashing.
If the problem persists you will need to access your Google Account through the browser, not on your Android, but on your PC and clear your data. I don't remember the exact steps that way, but I did find info in the help files there.
The only other solution from there is to do a factory reset, just make sure you do a backup of your device before resetting. Only do the factory reset as a last resort.
Edit: one more thing you can do is run a logcat, basically a running list of what is happening at specific times during application operation. I'm not qualified to give you the right means of accomplishing that, just too much info, but I have found a wonderful write up from the XDA forums on this.
This should show at what point the app is freezing and what is going wrong.