i have the same problem with my xecuter 3 and xbox 1.6b (see my topic below) i can't get in the flash menu. i thing i'am getting an other chip
If you flashed your X3 with the wrong bios no problem to get back to the flash bios screen reset your xbox in the 256k backup mode this will put you back in the flash bios screen. press and hold the power button and disk eject button and the little X will turn purple. then reflash with the 1.6v bios. that is the best part of the X3 if you make a mistake you can fix it.
If you still cant get into the bios screen then you need to check the solder joints on the LPC rebuild. go to team xecuter and the have a tutorial on this.
Dont buy a new chip just yet.
Hope this helps.
dont forget to reply on your results let us know how you made out.