I'm not sure if there are any known issues as far as music goes between the different versions of MKT released for PSX, but I have the Greatest Hits versions (the latest) and it plays music just fine on the PS2.
I had the same problem with the MKT. On the PS2 the music cuts but on my PS3 (slim) works. But the bad part is when i pass the game the screen turns black but the music still plays. same when (Press start to continue) as soon it goes to (0) GAME OVER the screen turns black. Am fixing to buy another copy from ebay soon.
If youre playing with the PCSX 2 Emulator, Mortal Kombat Trilogy has a known compatibillity problem regarding is Music CD Access. It will not work (unless they fixed recently). You could play the PC Version on DOSBOX if you own that version