Nintendo has two forms of revision numbers that they use for their cartridge games. The first one is the "-n" identifier on the end of the serial number which means that something physical about the cartridge has changed. In 99% of the cases this is an update to the label.
Back in the mid-90's we saw a lot of "-1" games appear because common games that everyone wanted to buy were being distributed when the ESRB was being instituted. There are many games that have a standard version and a "-1" revision simply because the ESRB rating was slapped on the label.
Nintendo's own Player's Choice logo is another good example of many label updates that required a new revision number because of the addition of the Player's Choice badge.
What you are really interested in is the ROM version of the game that is on the memory chip on the PCB. For quality control Nintendo does mark their games with a ROM ID on the outside of the game. For any cartridge game with a label on the back (NES, SNES or N64) there is an impressed number on the sticker. For games with only a sticker on the front (GB, GBC, GBA) the number is impressed on the game label, with the exception of the DS and 3DS, which also have the revision stamped on the back.
This number represents the facility/manufacturing line that the cartridge was assembled on. If your cartridge has the first version of the original ROM you will only see the 2-digit facility number. However, if a new version of the ROM was released from the developer to manufacturing, then a letter was appended to the end of the facility code.
The first revision will be an "A", the second revision will be a "B", and so on. If you take a look at these identifiers you can determine which version of the ROM is on your cartridges. If both games have no revision code, or if they have the same revision code, choosing which game to keep is up to you.
The ROM version can be a bigger deal than the serial number variation, depending on the nature of the ROM change. Nintendo has been known to adjust the art in some of their games for no apparent reason. Choosing which revision is a matter of preference.
You may be wondering where to find out information about specific cartridge ROM variations. The best place to go for a detailed log of variations to game ROMs is The Cutting Room Floor. (Beware, this is a blackhole for retro-gamer nerds, such as myself!)
To be clear, this site DOES NOT distribute game ROM files but they have thoroughly documented differences between the software variations of many games, old and new, for Nintendo and many other systems.
The only unfortunate aspect of TCRF is that they do not claim which revision ID stamped on the game goes with which revision detailed on their site. Instead, they just say "Japanese Version 1" or "US Version 2" when outlining differences of ROM versions. You may have to read the details on specific revisions to determine which ones may exist on your cartridges but that's never a difficult process.
Batteries are best stored at temperatures of 20°C / 68°F.
More specifically, a battery provides more power at higher temperatures due to faster chemical reactions, which also speeds up self-discharge and reduces the battery's life.
At low temperatures, the opposite happens, and the battery can actually hold its charge for longer. However, since chemical reactions are slower, the battery also produces less power. This can lead to the powered device to run out of power much faster, until ambient temperatures rise. At low temperatures batteries also risk freezing to death.
So the first step to prolong battery life is to avoid storing them in places that can get very cold, such as basements or cellars during winter, or places that can get very hot, such as near a window during sunny summer days.
If you're willing to delete all of your savegames, you might as well store the cartridge in a cold environment (beware of frost damage), though that may not necessarily be good advice depending on the battery. The cartridge itself won't mind getting boiled or frozen (but it won't like getting roasted), since SNES cartridges are made of Nintendium.
Sources:
http://batteryuniversity.com/learn/article/discharging_at_high_and_low_temperatures
http://en.wikipedia.org/wiki/Battery_%28electricity%29#Storage
Best Answer
I'm not sure if you can apply it here, but I know there is a way to fix damaged paths on circuit board. Here is the link that demonstrates how to do it:
In short, it describes how to remove the damaged section of a circuit trace, which tools to use and how to replace it with a new trace.
In your case, I would first try to identify which paths are damaged. You can use continuity test of a multimeter for that. Almost any digital multimeter has that option nowaday. And then, you can apply the method described above on each such path.
You might need neurosurgical skills to do it on such a small board, but it should be possible.