What did I do wrong?

Hello, well I have an iphone 4 att 16 gb. The home button wasn't working on it so I decided to replace it and all. It was successfully but something went wrong. As I was putting in the battery back in the end to "test" out the iphone. The little plastic flap with the hazard sign was stuck folded back and I forgot to unfold it when I put the battery back. So I decieded to pull the battery out again. I was gently going to open the battery tab to disconnect the battery and for some reason, the battery tab came out.

Now I thought, oh well if I at least put it back into position the battery tab, it would fit in and be sort of "fixed". I plugged in my iphone to the wallcharger, it turned on my iphone and suddenly the ios 6 sign comes on... I use an iPhone 4S now so I haven't really updated this one that I was fixing. Afterwards, I slide to open bar on the ios 6 screen and then the next screen has the "connect to iTunes" image. So I do that, but after I disconnect my iphone 4 from the USB cord, the iphone shuts off. Weird I though and then I connect it iTunes in my computer, but now my iphone keeps turning on with the apple logo then off like less 5 seconds repeatably. This was my 4th time opening up my iphone 4, but now this thing happened I don't what to do really.