Problems while installing car stereo.....help!

I am trying to install a Kenwood KRC4003 into my 77 Grand Prix. It is a shaft style cassette receiver. I have been having a couple problems throughout the install. First off, when I was wiring for the power, memory and ground, the unit would not power on. Power wire was to a switched source in fuse box, memory to an unswitched source and ground was to the metal dash frame. No power. I was using a test light to check wiring and accidentally hit the radio chassis. The unit flashed on, and when I grounded the actual chassis of the radio, the unit would work. I also noticed that when I mounted the rear mounting brace to the dash frame, it would also get power. So I wired up the speakers according to the manual and checked it again. Its getting power and holds memory, but no sound to the speakers. I pulled the unit out to go over the wiring and now it did not need any type of chassis ground as described above, it stayed powered. The manual describes a BTL hookup for a 2 speaker application; left front positive and left rear negative to the left speaker, and right front positive and right rear negative to the right speaker. I used the old stereo wire diagram to tell me which wires from the car go where. I then took the speaker wires apart. Since I did not do the old install and I am not 100% sure of the wiring, I tried a set of speakers that I had laying around directly off the new radio wires. Same hookup as the manual called for...no sound. I even tried both left rear wires to the same speaker, etc, and still nothing. I can't figure out if I am missing something or if there is a problem with the radio. Everything worked with the old radio too. I already have a Kenwood KRC2007 shaft style in my 78 Formula and really like it, so I would really like to make this one work. Just hoping I don't have to end up having it fixed. I hope this explanation makes sense, if any clarification needed, just ask. Any help would be appreciated. Thanks!!

sounds like the ground wire going into the radio is suspect.

there may be a physical switch somewhere that turns the internal amp off.