If that doesn't work, try un-installing the whole game then installing it offline. One you have it up and running - then connect to the internet and download the updates.
I said screw it . I went and got a ps4 since ps3 has been nothing but disappoint.also ps3 is losing alot of online support. I recently bought socom confrontation wich is not Even playable! Because Sony shut down their servers. I gave my gta5 and 4 to my sister and brother in law they have a older ps3. May be it works for them.
OP the same thing happen to me with my 2nd PS3 not that long ago. never did find the answer to why it just stop loading into story mode, If i was to take a guess maybe the hdd was starting to fail? But whatever it loads just fine on my new ps3.. Which doesn't matter now since i got the ps4 version