ok so you don't need to put the pre amp to the computer. you need for it to come out of the reciever. your dilemma is that you aren't able to play the instrumental song with the mic.
this is how you should be connecting them to get what you want. scratch the whole idea of putting the sound through your computer.
you have the preamp, you plug in the rec, line out with RCA to RCA 
to the receiver. Plug it into the red and white inputs of a reciever.
now get your laptop. This is assuming this is the source for the video and audio for karaoke. use the cord mentioned before and instead of plugging the headphone jack into the line in, plug it into the line out of your computer.
plug the red and white plugs into the AUX line in inputs on the Pyle.
plug in your mDP to HDMI connector to the TV.
Now turn everything on. The video and sound will play from the MPB but the sound is being directed through the preamp which then picks up the mic and then the preamp take the sound from the computer and the mic sounds and sends it to the receiver which is then playing both the audio and video. The TV is playing the words and will be synced to the song perfectly since the computer is playing all the media at the same time.
I imagine there are other ways where you could have just the HDMI coming out of your computer but then you would connect your TV's sound output to the auxilry input of the Pyle.
I would try either method, but I wouldn't run the sound through the computer. the computer.