If the internal battery has run dry can I still find shinies and migrate..

I have the same issue, my gameboys battery has run dry, is thier any way I would like get a new battery er sumthin and, what does this prevent me from doing, it says time based events wont work, what does that mean?

You should be able to still transfer. I have on my sapphire game with dry battery. And for shinys you can still catch them but it's harder or easyer depending on your preference it will be more like trying to get a shiny in emerald than sapphire or ruby

Okay this has nothing to do with the game-boy itself. Pokemon Sapphire contains a battery inside it. If you flip the game over and look at the back, there should be a three-pronged screw. Manage to unscrew that, and you can than get into to change the battery, which greatly resembles a watch battery. I hope this helps.