Motherboard Broken after fixing screen?

Hi All!

So, I recently cracked my iPhone 4s screen and decided to try and fix it myself. Well, it didn't quite go as planned and I ended up ripping one of the ribbons that connects the screen to the motherboard of the phone (I believe it was the digitizer one) and the screen was completely black.

I took my phone in today to a cell phone repair place to see if they could fix the screen for me this time as I didn't want to screw it up again.

Well, it turns out that I also broke a tiny little piece on the motherboard that the repair people said is supposed to get a signal to my phone (I want to say it connects to the battery?).

So, I'm sure I would need to get a new motherboard, but would I need a new battery as well? Can I get any motherboard or are they specific to the cell phone carrier I have? How much would this cost me? Am I better off just getting a new phone?

Sorry for so many questions, I figured I would ask them now so I don't forget to later or not get all the info I need. Thanks all!