Data missing - Ipaq model HP5555 - did not do hard reset

Hello,

I'm sorry but the HP Ipaq 55xx series store data on a volatile ram based memory. Unlike a nand flash (like usb sticks, memory cards etc) this memory will hold data only as long as it's powered on. If your main battery gets empty you should still be able to retain your files for some 10-20hrs with the backup battery (if it's ok itself and not depleted). After this time the power to the ram memory is cut off and all data is lost.
The problem you face is somewhat related to that backup battery, as it appears it's unable to do it's job and maintain the power to the ram memory at least some 10 hrs. You should have that battery replaced.

There is no way to recover the data from the ram memory as it is stored as an electric charge over some memory cells in the ram chips. When there is no power, these charges dissipate and the pattern is lost.

I'm sorry for having to give the bad news.
Bogdan