I fought on the side of the Stormcloaks. Fought all the way through the battle for Solitude. And yes, the bug started for me. I started to look online and saw that A LOT of people had this problem. However, all the solutions were given for the computer version of the game. None were for the PS3 or Xbox versions. I thought it was hopeless.
So I reloaded my game, right before the battle and fought it again... However this time I decided to follow Ulfirc (sorry on spelling his name) to wherever he was going. This lead to one of the longest, slowest walks EVAR!!!
It lead all the way out of Solitude, down the hill, to the East Empire Company Warehouse area, underneath the huge overhand of Solitude. And this is the weirdest part of all. Ulfric decides to go for a swim!!! That's right a swim. So I followed him. A couple of times having to come up for air. This is because he dived deep into the ocean. Being an NPC, he can't die... I can!
Anyway, he then comes to a shallow spot and as soon as his head popped out of the water, he said the words "Go with the Gods." And just like that, the battle music was gone and the ambient music was back!!
What I'm thinking is that he was supposed to say this to me way up in Solitude, but didn't because of the glitchy nature of the game. So as soon as he said it, bam!!! Battle mode is done. But that's just my speculation.
Hope this helps some people, and sorry for the long explanation, but I wanted there to be a lot of detail for everyone.