See here for more information about original batteries and inner working.
Replacing by standard lithium battery
Replacing the battery will probably cause the backup RAM to be corrupt. Forget about your hi-scores and settings if you don't provide 3V on BATVCC while replacing it.
The battery can be replaced with an equivalent 3.6V NiCd battery or 3.7V rechargeable coin cell (LIR2032 or ML2032), but the 470 ohms (yellow-purple-brown) charging resistor must be removed if a non-rechargeable battery (such as a common CR2032) is installed.
The resistor can be added back if a rechargeable solution is required later on.
Replacing by rechargeable battery
Original battery can be replaced buy modern lithium and ni-mh equivalent.
- LIR2032: search for "lir2032 tabs"
- NiMH 3.6v: search for "nimh 3.6v tabs"
DON'T TRASH THEM
Batteries contain a number of heavy metals and toxic chemicals. Disposing of them in regular trash leads to soil contamination and water pollution. Please send them to a local collect point.