After a long period of not using the iPAQ, the battery will not charge, the power monitor reports the battery charging but when external power is unplugged there is no power. Is the battery 'dead' and in need of replacing or is there some other common problem ?

Yes you can buy them on e-bay here is the link for one
http://www.ebay.com.au/itm/Charger-For-HP-iPAQ-hx2100-hx2400-hx2490-hx2750-364401-001-367205-001-/360527673086?pt=AU_MobilePhoneAccessories&hash=item53f11fb6fe just charge up the battery externally and away you go I bought a second battery so I can have one on charge charging while I am using the one in the IPAQ so no down time

Have you seen inside a laptop battery, it's not just a battery. It also has control circuitry inside, could be that. Not usually repairble but you can do some makes of battery. See here:Circuit.
Personally I would buy a new battery.

its just 3 things.
1; battery
2: charge regulator on the device.
3: power pack
one is bad.
so its not battery, now its #2 or #3

seen the regulator is toasted
very common
why not buy as used spark same device, and mix part to get good
or ditch it and upgrade,

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.

Ufortunately, the battery is likely the culprit.
You can try removing the battery overnight, then leave on charger for at least 12 hours.

These batteries generally require replacement every 1-3 years. They deteriorate quite rapidly if left unused/uncharged for extended periods of time (like a year!)

Failed battery pack most likely.

How to correct iPAQ 5450, 5455, 5550, 5555 battery charging problems / dead unit syndrome.

The iPAQ 54xx or 55xx will not power on if the batteries charge is lower than 3.2 Volts, if your battery charge falls below the 3.2 volts level your unit will not turn on, you need to plug the iPAQ into a cradle or AC charge adaptor. Note the charging light on the iPAQ will not flash at all (normally flashes orange) until the battery charge has reached a minimum charge level of 3.2 volts. You then need to perform a normal reset, then the unit should switch on normally.

HP Procedure is as follows:

To charge and reset the iPAQ Pocket PC h5400:

i) Connect the iPAQ Pocket PC h5400 to an A/C power supply.
ii) Charge the battery to the minimum level of 3.2 Volts. This will take 5 to 30 minutes depending on the current charge level.
iii) Perform a normal reset.
iv) Power on the iPAQ Pocket PC h5400

It is recommended that you keep the iPAQ Pocket PC connected to the Universal Cradle or Cable when it is not in use.

For me I prefer charging the iPAQ using the usual cable, not the USB as I had some troubles with that It makes the battery drain faster. So Use a usual charging transformer.

In this model of ipaq the battery come inbuilt which means it is not enduser replaceable so cannot place an order to the battery so call HP and send the unit in for service. All the best :-)

When you charge up your iPaq, do you use the cradle, or do you use the AC-adapter with the little iPaq power converter that came with the iPaq? Try both, and see if it charges up your pda. Try and borrow an iPaq car-charger and see if it charges up that way (the ones that do not need the iPaq power converter). If you are lucky enough to power up the iPaq even for 2 minutes, enable USB fast charging in the SETTING -> BATTERY. Your USB-data-cable or cradle will then be able to charge it up that way...