The following is a complete over simplification, and yet completely true:
1) If you attempting to mix a dry vocal into a completed, full (dense) mix - it won't work.
2) If you attempting to mix a semi-wet vocal into a completed, full (dense) mix - it won't work, but not in the same way that #1 won't.
3) If you attempting to mix a vocal (any) into a completed sparse mix (drum machine, bass, and maybe some noisy thingy that functions as a melodic device) - now you have a chance.
The difference is that the completed (dense) mix was made to sound great without the vocal you are trying to add. All the decisions about what frequency range is given to what instrument, and how much space that instrument will take up in the mix was made without the MAIN focus of the song - the vocal.
I don't know your age, but in movies made before 1995 or so, the way that most "talking while driving" scenes were done was to use a screen behind the car (a fake) where the actors sat. They would project (either as rear projection or as green screen composite) pre-recorded footage of the road moving on the screen and film it with the actors. Viola - the actors are now in a car going down the road. The problem is, there is no interaction between the two. Sure, they shake the car when it hits a pot hole, and maybe do some moving lights across the actors to simulate passing headlights, but who was fooling who? Seriously, take a look at Terminator 2 when Arnold, the kid and his mom leave LA in the car. That movie had more cutting edge special effects and that scene looks like it was shot in 1930 (I wonder if they fixed it for the DVD releases like Lucas did..). ANYWAY - the problem is that the foreground (the actors) and the background (the outside) don't interact the way they should. Your eyes know.
In this case, you ears are telling you "That doesn't sound like what I hear on the radio" (that might be a good thing...but I digress). With a sparce instrumental mix, it is much easier because there is so much room left in the "tall" aspect of the mix. This is why early funk records were used as loops for the beginnings of hip hop. They were pretty sparse and you could put them into, under, or on top of other tracks with greater ease. Much of hip hop is still sparse.
When you make a dense mix, you are always pushing and pulling things to make them all work. There is only so much space in the mix. If you have a midrange heavy vocal you pull some mids out of the guitars. If you have a long sustaining 808 kick, you can't put a bass guitar down there too. You will carve out the bass to let the kick come through, or pull a chunk out of the kick to let the bass guitar come through. Many times, you do BOTH. They interact with each other.
Finally, you said that your attempts didn't work. Since there isn't a "make it work" button on my console, the solution to your issue has other topics - dynamic range, stereo width, etc. You could always transcribe the back tracks, create them in Logic, and then put your vocal in. This would make sure you could mix around the vocal from the ground up.
If all of this is too much work or not understood; compress it hard, de-ess it, and give it a stereo delay to taste...