WP 34S will not turn on

[BarryMead]

Latch UP. Most modern CMOS, and NMOS devices have what are called "Input Protection Diodes" to prevent electrostatic shock from damaging the circuitry. These diode pairs provide a low impedance path (diode on) when the voltage at an input goes above VCC or below GND. The configuration of these diode pairs is very much like that of an SCR (Silicon Controlled Rectifier) and can "Latch Up" into a high current state if the battery voltage ever falls below 2.3 volts (when a 3 Volt input exceeds VCC by .6 to .7 volts). Anyway if the calculator ever gets into this "Latch Up" state the only way to get it out of this state is to remove the batteries and short the VCC and GND pins of the battery together for a few seconds to bleed off any residual charge held in capacitors.
It might be worth a try to remove all power from the calculator and short out the battery terminals for a few seconds before attempting to re-apply power. If the current draw returns to a few micro amps then you may yet be able to salvage your calculator.
Although even then it might still be less trouble to ship it to someone who owns a JTAG programmer or buy a new one. Best of luck, Barry