In attempt to clear the expired ink code on a HP Photosmart 8250, the display screen is not working after reassembling it.

SOURCE: HP PHOTOSMART 8250

did you take the tape off the cartridges? and are set all the way in?

SOURCE: Expired in cartridge

I had the same issue with my Photosmart so I checked the HP web site and they said that some cartridges (including HP02) expire but you can override. Try opening the top of the printer and undoing the cartridge latch. Then relatch it and close the top. Worked for me (at least for now)

SOURCE: 8250 HP INK EXPIRED MESSAGE

I had same problem, and i solved it.
I opened my hp 8250 and removed it`s battery. It is located on left side of the printer, on the main board. You need to remove plastic covers , and then remove 3 screws holding board. You can move board just enough to get damn battery out of there. Now it works perfect!
I can send you some piccs if you need help.
Regards
Sasa

SOURCE: HP Photosmart 8250 Support Menu?

I have the same issue with the printer but I do have a solution for you.
I do know how to reset the error codes.

Start by turning off the printer and unplugging the power cord.
Next, you need to hold the Instant Share and Photo Tray buttons simultaneously while plugging in the power cord. If done correctly you will see the LCD Screen turn green with the numbers '1 2 3 4 5'.
After that is done, you need to unplug the printer, and replug it.

I myself have not been able to resolve the issue as to why it is giving me the error code. Any help would be appreciated.

SOURCE: Keeps stating ink expired

i guess your printer has reach the printing warranty.. try to search in the web on how to reset your printer, ^^