First recommendation before you continue reading - don't do it before reading the hpmuseum.org forum and check that is fine to do it!
I have given information about the last firmware update, that was made available on May 28. I did it that same day.
The day after I found the calculator dead. I mean, all the battery had been drained, and it needed to be connected to USB to work. Looking into the hpmuseum website, I found that the first release of e firmware upgrade had a problem with power management. The calculator entered into a high power consumption mode until the battery was off - independently of it being switched on or off. HP's recommendation was to immediately upgrade it to a yet newer firmware.
This second upgrade was not easy. The system continued believing that the calculator didn't need an upgrade (“there are no updates”), and going through the forum helped me to know that I had to delete the previous files from specific folders in the HP connectivity kit, so that the system was made to think that there had been no upgrade.
Somehow, I did something wrong along the way, probably an incomplete update (the USB connection is known to stutter sometimes in the Prime), and my system could not start up before crashing in 5 minutes. It showed the HP logo, the known “x2+y2=1” and the circle around it, and then it crashed again. There was no way of exiting that loop. Thanks to members of that forum, I was able to put it in “recovery mode”, but then I needed to upgrade it with a manual method (the “upgrade.exe” program), since the hp connectivity kit did not see it. And there is where I failed. I should probably been conservative and enter a prior firmware - instead I entered the very latest one, and completely blocked the machine. Now it won't start at any rate. Even taking out and back in the battery pack. Dead for all practical purposes. Let's see tonight what the forum gurus say on how to revive it.
I know for a fact that another customer of us has fallen in he very same trap. So, I end as I started this blog entry: don't upgrade yet!