Before you start worrying about transmit power supply requirements you need to get the radio to receive and give you squelch noise.
I will give you my trouble shooting technique with a radio presenting these problems. First verify you have a minimum of 12.5 volts at your power supply. Next make sure of your connections to all the power leads. The main big red lead, the orange and green leads all go to positive 12.5 volts, and of course the big black lead which is ground. If you have fuses in any of the lines verify they are good or make sure you have 12.5 volts on the equipment side of the fuse. BTW all Motorola radios come with positive ground warnings, so I would not be too concerned about that yet.
Next verify the connection to the radio trunk pack itself, the radio heads will light up, and even give you a transmit light with no radio connected. Next verify the cable connections on the back of the head boxes, make sure they are in their correct spots, its possible, but not very likely that one may be swapped or loose. The A B zone lights are lit up from behind, so the may come on or not if the bulb is bad, the frequency selector do not have back light bulbs, there should be just one bulb in the center of the board.
While it is a bad sign in a Spectra a popping sound when you turn on the Syntor radio is a good thing, that tells you you have 12.5 volts to the main red lead, which powers the transmitter and the receiver audio amplifier. If you get the pop, adjust the squelch control to one extreme then the other for squelch noise, if no noise make sure the radio microphone is not in the hang up box, because if the radio is set up for PL it will not unmute.
If after you run through these checks, and the radio still won't power up you are going to need a service manual, since you will have to start checking the voltage regulators in the radio.
If you do get the squelch noise your half way there. Now you can worry about current capability of you 12 volt supply. For 110 watts out, the radio will draw about 32 amps. You can lower the power out by adjusting the current limit and power out pots for the capability of you supply.