I know, probably tried this but:
1) get a new cell.
2) remove old cell.
3) short the +ve to the -ve to ensure no remaining charge in system or let sit over night.
4) install new battery.
5) the battery cover has the letters AC and an arrow.
6) When the new battery is installed, short the AC battery cover to the point the arrow points to.
This should remove any confusion that the IC may have due to a static shock or low battery.
My HP01 had an absolutely bizarre display and I thought like you, OHOH but following the above procedure I resurrected it. I actually had to leave it without batteries for a few days too remove all residual charge in any of the capacitors.
Geoff
Is this the one?
http://www.haq.watch/Casio%20SP-400%20Gallery.html
Edited +ve and -ve (stupid autocorrect)