OK, you've definitely got a cheapmod, but most cheapmods only have 1 wire, you claim yours has 3. Can you describe where each of the wires go to/from?
It sounds to me like your chip is a cheapmod fitted with an IC that allows you to enable/disable the chip, and possible enable/disable flash protection using the Power and Eject buttons of your Xbox. Try booting your Xbox by doing each of the following, and take note of what happens each time. I'll use P for Power button, and E for Eject button.
1. Tap P
2. Tap E
3. Hold P for 1-2 secs
4. Hold E for 1-2 secs
5. Hold both P and E for 1-2 secs
6. Hold P for about 6 secs
7. Hold E for about 6 secs
8. Hold both E and P for about 6 secs
I guessing that one of the above will boot your Xbox with the chip disabled, and another one will boot the Xbox with the chip in Flashable mode. Try flashing after trying each of the above boot methods.
Let me know how you go.