First, make sure you have 8+GBs free for the Rage install.
However, what you're explaining sounds like what happened to me with Resistance3. I shut off the console while it was installing the game data because a video was playing and I didn't know it was actually installing anything. This corrupted the data and loading the game kept hanging similar to what you are explaining.
The fix was to go into the ps3 cross menu / game data folder, find the resistance 3 data(in your case Rage),and then delete it. One problem I encounter was that it took a long time to delete. At first i wasn't sure it was actually working(deleting) so I tried this:
Fixing Ps3 File system
1.turn off ps3
2. Hold the power button down; the system will turn on and turn off once again.
3. Once the System has been shutdown, re-press you finger until you hear 2 consecutive beeps
4. When you hear the 2 beeps take finger off power button.
5. You will be prompted to plug in your controller via USB and then hit the PS button
6. The Recovery menu will pop up.
7. Select "Restore File System" from the Recovery menu.
8. Agree to restoring the file system.
I think it was option 3 or 4. I would NOT recommend reformatting or reseting the entire system as you will lose all of your data, games, and saves for the entire ps3 system. It will warn you though, so be careful.
Even after I did that, deleting the corrupted data still didn't seem to work and just seemed to sit there like before. I let it go overnight and when I got up the next day and started the system, it seemed to work. The corrupted data file was gone and I could install the game data correctly.
So, perhaps try deleting the data first and let it go for an hour at least before trying the "Fixing the PS3 File System" trick I mentioned above.