The internal battery in the cartridge is dead. It's what cartridge-based games used to save data on, in place of a memory card.
So, you/your friend/the original topic starter/whoever will have to open the cart and change the battery. This is difficult, as Nintendo carts have custom 'flower' screws in the back, that are hard (but not impossible) to get open without a Nintendo screwdriver. I had my brother get mine open with a little pair of plyers (sp?). Anyways, once you get it open you'll see the battery inside, and it *should* have a model number written on it. Take the battery with you to your local hardware store/Radioshack/wherever, and find a new one. The one I bought for Gold Version was $3. Replace the battery and voila. It should work. If, for whatever reason, it doesn't (I had a copy of Super Mario World that had this problem, but it didn't seem to be related to the battery), then the only real option is to get a new copy.
Alternatively, I've read somewhere that Nintendo will replace any drained batteries free of charge, provided you pay for shipping and such. Consult Google for more on that.
Given the amount of work involved, and Blue Version's age, it would probably be easier to just buy a new copy off eBay, or just emulate it.