Due to the age of the camera your problem is not the battery but the release capacitor located on the bottom of the camera when you remove the bottom plate. You can replace this capacitor yourself, just unsolder the old cap, but pay very close attention to the polarity of the cap when removing so you can put the new cap in place the same way. Put fresh batteries in and it should start working again.
I have 13 years experience in repairing camera equipment and i used to see these come across my bench a lot for the same problem you are describing.