When i turned on my gameboy color today it showed up on the screen after the start part a weird battery symbol comes up on the screen then.

That's normal. The gba will play all three generations of game boy games. The start up screen that comes up is that of whichever cartridge you are putting in.

Well its because the battery inside of the gamepack that allows you to save the game data is dead by now and needs to be replaced.

Its beacuse that it might be broken then.

Okay, the white crusty stuff that was on the batteries is actually acid and corrosion from them being connected but not in use for so long. What you need to do is take out the batteries and CAREFULLY clean all the leads in the battery compartment. I say carefully because going at it with a spraybottle and a towel isn't going to get you anywhere. Your best bet is Rubbing Alcohol and Q-tips (cotton Swabs)

you need to get a game boy advance and it will still play those games

Are the batteries new?

Insert the game before you turn on the gameboy. Try blowing air in the connections area of the game and in the connections area of the gameboy itself.

possibly water damage... there might be an indicater of this such as one on a cell phone. behind the battery possibly, a small sticker that changes color when dampened.

as for solutions... warrenty? lol

It sounds like you need to put in a new set of back-up batteries. They can be found behind where the AA batteries are.