Your battery is over 14 years old and doesn't see regular use. Its probably not holding a charge anymore. Someone can correct me on this, but I'm pretty sure the average oem style battery is supposed to be replaced every 5 years or so.
Replace it, its not going to effect the collectibility of the car. If you really think having the factory battery will be important then just stick it on a shelf and use it for the times you have the hood up for show, or plan on selling. But use a good battery for driving. Otherwise you risk getting stranded.