It appears that you left out a sentence. Did you mean to say with the white and bare wire from the cooktop connected the bare from the supply cable that the cooktop did not function?

Faulty ground (bare wire) connection or faulty cooktop would be my first suspicions.

I had suspicions about the cooktop as well and I took it back and for another unit, and it still does not power on, I suspect that the ground wire could possibly be faulty however i hooked the old unit it powers up correctly, could the old unit have been functioning with a faulty ground the whole time ? kinda at a loss at this point.

Did your old cooktop have the same types of controls, lights, timer, clock etc. as your new one? The heating element itself does not need a neutral or ground. Newer cooktops often have more sophisticated controls that do. If you have a meter, start by checking for voltage between a hot wire and the grounded/bare wire.

Your correct the old one did not have controls like the new one does, i believe that since i dont have true neutral this new unit is not gonna work, i dont have the option to rewire either since the cooktop is in a island and the wires run under tile, might have to go with the same setup that i had before....

The fact that the new cooktop did not work when you connected both the white and bare wires from the cooktop to the bare wire from the supply cable means that you have a bigger problem with the house wiring itself. (It should work) Your entire grounding system could be messed up. This can effect the efficiency of other safety measures in the electrical system, such as the breakers may not trip when necessary, resulting in a fire. You need to have this fixed by a qualified electrician who has the ability to track down the problem. Then, you can keep the cooktop too. The next one you try may not work either.

250.140 Frames of Ranges and Clothes Dryers. Frames of electric ranges, wall-mounted ovens, counter-mounted cooking units, clothes dryers, and outlet or junction boxes that are part of the circuit for these appliances shall be connected to the equipment grounding conductor in the manner specified by 250.134 or 250.138.

Exception: For existing branch-circuit installations only where an equipment grounding conductor is not present in the outlet or junction box, the frames of electric ranges, wall-mounted ovens, counter-mounted cooking units, clothes dryers, and outlet or junction boxes that are part of the circuit for these appliances shall be permitted to be connected to the grounded circuit conductor if all the following conditions are met.

(1) The supply circuit is 120/240-volt, single-phase, 3-wire; or 208Y/120-volt derived from a 3-phase, 4-wire, wye-connected system.

(2) The grounded conductor is not smaller than 10 AWG copper or 8 AWG aluminum.

(3) The grounded conductor is insulated, or the grounded conductor is uninsulated and part of a Type SE serviceentrance cable and the branch circuit originates at the service equipment.

(4) Grounding contacts of receptacles furnished as part of the equipment are bonded to the equipment.

" i believe that since i dont have true neutral this new unit is not gonna work,...."

I believe this is correct. Unless your cooktop instructions tell you that it can be hooked up with a 230/240 circuit, you need a 240/120 or 230/120 to make it go. Time to get a different cooktop or tear up the tile.

"The new cooktop has a black, red, white ,and bare. I connected the black to black and the red to red and the white and bare together to the existing bare as per manual."

250.140

Exception: For existing branch-circuit installations only where an equipment grounding conductor is not present in the outlet or junction box, the frames of electric ranges, wall-mounted ovens, counter-mounted cooking units, clothes dryers, and outlet or junction boxes that are part of the circuit for these appliances shall be permitted to be connected to the grounded circuit conductor if all the following conditions are met.

(1) The supply circuit is 120/240-volt, single-phase, 3-wire; or 208Y/120-volt derived from a 3-phase, 4-wire, wye-connected system.

(2) The grounded conductor is not smaller than 10 AWG copper or 8 AWG aluminum.

(3) The grounded conductor is insulated, or the grounded conductor is uninsulated and part of a Type SE service entrance cable and the branch circuit originates at the service equipment.

(4) Grounding contacts of receptacles furnished as part of the equipment are bonded to the equipment.