There's no hint of either a battery or a capacitor being used for data retention on the PSR1500/3000 - I have the service manual - nor do I recall seeing a battery inside my 3000 on the various occasions I had it apart (to replace the LCD, fix video out, change keyboard contact strips).

The internal memory is described as flash EPROM. If the 1000 is the same technology I'm afraid you could be in trouble.