I'd recommend few more things as well, in this order:
1) Make sure the battery door lock is locked. If it's not locked the machine won't do anything.
2) Soft Reset (Just press the stylus into the small hole at the bottom, to the left, near the power/cradle connector.
3) Take the battery out and wait 5 minutes, then start at 1 again.
4) Try leaving the unit plugged in for 30 minutes or more, then start back at 2. (By now you should be sure your battery door is locked
)
5) Hard Reset (Press and hold Contacts and iTask buttons, then press and release the reset (with the stylus). Wait 3 seconds, then press the reset again. (The first sequence is a hard-reset. The second is a soft-reset to get things started again. The hard-reset basically disconnects the battery and shuts the unit completely off. The soft-reset wakes it back up again (we hope)).
6) Contact HP or
Pocket PC Techs for diagnostic servicing.
With the age of the hx4700, it's possible the battery has gone out. If you have another hx4700 nearby, by all means try the other's battery before resorting to anything beyond the soft-reset and battery door lock check.