The unit charges fine, but the second I press the talk button it goes dead!

Let's try to reset the charger system.
Step 1: Unplug from the charger, press and hold the Power button for 30 seconds
Step 2: Plug into the charger. Press and hold the power button for 30 seconds
Step 3: Let charge for 12 hours
Step 4: Unplug form the Charger, run the Kindle until totally dead.
Step 5: When DEAD. Press and hold the power button for 60 seconds.
Step 6: Plug into the charger, let charge normally
If this does not reset the charging system you have either a faulty Kindle or a faulty charger, contact Amazon for replacement.

I had this happen to me on one occasion. Pressing the power button any number of times would not turn on the unit. Also, plugging in the car charger did not turn on the unit or charge it either.
I found that holding the power button for 10-15 seconds forced the unit to reboot, and it started just fine after that.
Since then, I've had an even more irritating issue, where holding the power button for 10-15 seconds would restart the unit, but it would freeze at the "loading maps." part. I ended up plugging the unit into my PC, which started it for purposes of data transfer. I then disconnected it from the PC and it restarted properly.
Try those out and see if you have any better luck.

I have had several people bring me in their units dead. You need to try a reset first. Connect the USB cable to your unit and your computer Press and hold the ON button and the PLAY (>||) button at the same time for 20 seconds.

Try charging the phone. They are usually shipped with a near dead battery.

Either the battery is bad or the battery needs to be charged or the charger is bad thus the battery isn't charged.

To power the unit back on, press the "Mode" and "Reset" buttons at the same time. Let go of those two buttons, press the power button, and the unit will turn back on."

I charged the unit and now it works fine. Plug into computer and charge for a while and the unit should work fine.

have you only been charging it with the usb cable?
try plugging it into a ac adaptor, (make sure the button is in the off position at the bottom)
and it should hopefully restart, then turn it to the on when it's loaded, and leave it plugged in till it's completely charged

that might work

I called and they told me,i have the same problem, to just turn the battery switch ( bottom thing) off and charge it over night via wall outlet. hope it helps im trying it as i type so i wouldn't know...

Try pressing the reset button, check your documentation for the location...but it's at the connection interface.