Unit will not power on all of a a sudden always have it placed in cradle when playing otherwise charging

Cradle and contacts are fine. Cradle circuit is nothing but a reed relay and few wires, relay closes on proximity to robot's body, therefore no voltage on contacts before robot is close to cradle.
There is a thermistor inside of battery, and mine was bad. I removed it and now I am charging the battery from my bench power supply at about 220 ma current, overnight, and it works. Probably the solution is to get a new replacement battery, but the one with the thermistor inside (OEM), easily recognized by the third wire, and all should be fine, assuming that nothing else is wrong with charging circuit or power adapter (12v/1A)
Hope this will give you some ideas of where to poke.
Once successful, please post your solution.

The manual, which can be found at: http://www.home-electronics.net/ge/pc/IB/25952EE1_IB.pdf, reads:
4. Place the handset in the base cradle. The charge/in use indicator turns on,
verifying the battery is charging. The unit will take 20 seconds to register
and verify its security code. READY shows in the display.
NOTE: In case of a power failure, the handsets may display
UNAVAILABLE when the TALK/CALL BACK button is pressed.
You must then place all handsets on the main base cradle
for 20 seconds to re-register.
That should reset your handsets. Hope this helps :) Thank you very much.

1. Plug the charger adapter into the charging port on the bottom of the HP iPAQ Pocket PC.
   Figure : Charging the battery
2. When the power indicator on the top of the HP iPAQ Pocket PC turns solid amber, the unit is fully charged and can be disconnected from the AC adapter (approximate time to fully charge a unit is four hours).

NOTE: The amber charge light blinks while the battery is recharging and turns solid (nonblinking) when the battery is fully charged.In the event of a low backup battery warning, charge the unit immediately before removing the main battery to avoid data loss. To view the amount of charge left in the backup battery, tap Start, Settings, the System tab, and Power.
Charging with the universal desktop cradle and AC adapter Use the universal desktop cradle to charge the HP iPAQ Pocket PC, or synchronize the HP iPAQ Pocket PC with a computer.
Follow these steps to charge the HP iPAQ Pocket PC using the universal desktop cradle:

1. Plug the AC adapter into an electrical outlet and connect the other end of the AC adapter to the AC connector on the universal desktop cradle.
2. Connect the serial or USB cradle cable into the appropriate port on the desktop PC.Figure : Connecting with the cradle
3. Slide the bottom of the HP iPAQ Pocket PC into the cradle and push firmly to seat it.

CAUTION: To avoid damaging the HP iPAQ Pocket PC or the cradle, make sure the pins are aligned before pushing the HP Pocket PC into the cradle.

Figure : Charging with the universal desktop cradle

1. AC adapter into electrical outlet
2. AC adapter into universal desktop cradle
3. HP iPAQ Pocket PC into cradle

NOTE: The amber charge light blinks while the battery is recharging and turns solid (nonblinking) when the battery is fully charged.There are stabilizers located in the universal desktop cradle that assist in aligning the unit when there is no expansion pack attached. When placing the HP iPAQ Pocket PC with an expansion pack attached into the universal desktop cradle, the stabilizers will be pushed down by the expansion pack. To release the stabilizers for use without an expansion pack, press the button on the back of the cradle.
Charging with the optional USB Autosync cable Charge the HP iPAQ Pocket PC using the optional USB Autosync cable by connecting the Autosync cable to the HP Pocket PC and the personal computer. The HP Pocket PC will be charged using power from the personal computer.
For more information on charging the HP Pocket PC using the optional USB autosync cable, from the Today screen, tap Start, Settings, the Systemtab, Power, the USB Charging tab, Settings, and Help.
Charging a low battery The HP iPAQ Pocket PC will not turn on if the battery has a low charge (less than 3.2 Volts). Fully charge the battery prior to using the HP Pocket PC.
If the charge on the battery goes below the 3.2 Volts as a result of not being connected to the universal desktop cradle or the AC adapter, no damage will occur to the battery. However, the HP iPAQ Pocket PC charge indicator light will not flash until the battery reaches the minimum charge of 3.2 Volts and a normal reset is performed.
Follow these steps to charge and reset the HP iPAQ Pocket PC:

1. Connect the HP iPAQ Pocket PC to an A/C power supply.
2. Charge the battery to the minimum level of 3.2 Volts (this will take 5 to 30 minutes depending on the current charge level).
3. Perform a normal reset by using the stylus to lightly press the Reset button on the bottom of the HP iPAQ Pocket PC.
4. Turn on the HP iPAQ Pocket PC.

Keep the HP iPAQ Pocket PC connected to the universal desktop cradle or AC adapter when it is not in use.

Same thing happened to mine. Put the unit in the cradle (just like you are going to recharge it) and press the reset and mode button at the same time for 3 seconds. This will "wake" the unit up.

BATTERY INSTALLATION AND INFORMATION
Your wireless headphone unit requires two rechargeable AAA batteries.
Rechargeable batteries are uncharged when you purchase them. Before
you can use the wireless headphones, the batteries must be charged for
16 hours. Follow these steps to install and charge the batteries.
Installing the Rechargeable Batteries
Take care to follow these steps to correctly install the batteries.
1. On the right headphone, locate the battery compartment (1).
Use the finger depression on the compartment to turn the battery
compartment cover counterclockwise to remove the cover.
2. Insert two AAA rechargeable batteries, carefully following the
markings inside to ensure the batteries are inserted properly, with
the + and - ends in the correct positions.
3. Replace the battery compartment cover.
Charging the Rechargeable Batteries
To recharge the headset unit, follow the directions below. Note: The
cradle/transmitter on the WHP141 is not a recharging cradle, although
you may place the headset in the cradle during recharging.
Follow these steps to recharge the NiMH rechargeable batteries.
1. Make sure the ON/OFF switch (2), located on the right headphone,
is in the OFF position.
2. Connect the AC/DC main power adapter to the DC IN power
supply socket (11), located on the back of the cradle/transmitter.
3. Plug the adapter into an electrical outlet.
4. Connect the charging cable (10), located on the back of the
cradle/transmitter to the recharging input (3), located on the right
headphone. The headphones can either be placed in the
cradle/transmitter or placed next to the unit. If the headphones are
connected correctly, the charging LED indicator light on the
cradle/transmitter (8) illuminate.

its the hardware error and needs reparing of the circuit getting short.

here is a movie on how to replace Garmin's battery


YouTube - Replacing the Battery in Your Garmin

Check the fuse at the tip of the power cord. Unscrew the round black plastic and this will release the fuse. Otherwise there could be a problem with the power cord. If the cord is defective, replace only a Garmin replacement.

Does the car charger cord plug into the cradle? or just straight into the unit (despite resting on the cradle) ? Do you know if anything else charges via the car charger?

I sent my battery back and it was replaced by the supplier. The unit is fine now so the only conclusion I can come to is that it is due to a faulty battery....