That really svcks , many PS3 users have been frustrated with "complications" with the GOTY but this is the first time i've heard of the game having loading issues the first load after turning on the console.
Check in the PS3's menu (saved game files) to check if the save file isn't corrupted. Personnaly , the only times this happens is when re-loading from the FO3 menu , and having the turn off the console then turn it back on but after that it loads fine.
If the music stops then it usually means the game freezes , what i do is hold down the PS button to see if the game really froze or if it justs lags. If by holding th PS button the controller turns itself off then it probably means it froze. Sometimes the controller menu appears which means the game was just lagging.
Longer load times with the GOTY is common , but this early in the game there shouldn't be any problems. Personnally , i rely on auto-saves much more , everytime the game starts to lag i wait an hour to autosave in case the game freezes , if it does then i simply re-load my autosave.
In other bethesda games , autosaving could be disabled to help the game freeze less , but only 2 hours in i highly doubt this would be a fix-all.
Maybe try a new game , maybe make multiple saves , as another user suggested make a new save file every level in case one file gets corrupted. Although in my extensive use of FO3 not once did a file get corrupted.
Sorry if this isn't much help.....