If the songs aren't showing up in the game it's because the DTA file is not at the right place. No matter if you have a modded console or not, installed rap file or not, if DTA file is where its supposed to be the song will show up in-game. If you don't have the rap file installed it will simply not load.
If you have a NTSC disc your DTA file and all the song's folders should be in "/dev_hdd0/game/BLUS30463/USRDIR/HMX0756/songs/" and the rap file should be named "UP8802-BLUS30463_00-RBHMXBANDCCFF0D6.rap" when installing.
If you have a PAL disc it should be in : /dev_hdd0/game/BLES00986/USRDIR/HMX0756/songs/ and the rap file should be named "EP0006-BLES00986_00-RBHMXBANDCCFF0D6.rap" when installing.
You obviously need to use the right rap file for the region.
That's really all there is to it.