On the back, model no states H3000. Is this the same for all dsp4000s?
Sorry, don't know. These are getting quite old now.
Any way to fix this?
Depends what sort of card it is. The most common type are pink, with a rather ugly "brain" image on the label. If this is it, hold it with the label towards you, and the edge with lots of holes to the bottom. Then lightly press into the hole in the top of the right edge with a paperclip or something. While doing this, gently pull at the right-hand size of the top edge using your fingernail. This will free the battery and holder. This sounds fiddly, but you will understand in time. The battery is a BR2325 – a local Radio Shack or other electronics shop should have one. If not, try Mr.Google.
Other cards may have a tiny crosshead screw which holds in the battery compartment.
If the battery is dead there will be nothing on the card. These are hard to find nowadays, so probably worth risking a few fingernails to try and get it running.